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• article
CHEN Bin;CHEN Mu-Fa;XIE Yingchao;YANG Ting;ZHOU Qin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.001

As the continuation and deepening of \ncite{1},this paper focuses on the center of economic equilibrium and uses mathematics as a tool to explore two themes in the economy: firstly, the pillar'' industry and bottle strength'' industry, top'' products and weak'' products in the economic system, that is, the ranking and
stability analysis of products; secondly, forecast and adjust, optimize the design and debugging of economic structure.

• article
CAO Xuefei; LI Jihong; WANG Ruibo; NIU Qian; WANG Yu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.001

The bi-directional long short-term memory neural network model is widely used in natural language processing, but hyperparameter tuning of the model is difficult in practice. In this paper, we take the semantic role recognition task as an example, consider four candidate features (word, part of speech, target word and position) and two hyperparameters (the number of layers of the network and whether CRF classifier is used) as factors in robust design, and select the optimal combination of features and hyperparameters by setting levels of each factor and performing experiments. In particular, we perform 32 cross validation on a small datasets to select the optimal configuration combination of the model based on the SNR of robust design. Then, we analyze the influence of each factor on the performance of the model by quantitatively analyze so that the model has a certain degree of interpretability. Moreover, in order to verify the superiority of our tuning method, we use the standard segmentation of natural language processing on a big dataset, adopt the traditional greedy strategy to select the optimal configuration combination, and compare with our method on the test set. The results show that our method is better than the traditional tuning method.

• article
BIAN Huabin; TONG Xinle; YAO Dingjun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.002

In the context of the aging population, longevity risk will increase great economic pressure to the national endowment security system. How to measure and manage longevity risk has become the focus of research in recent years. Based on the Chinese population mortality data, and Lee-Carter model, we introduce DEJD model (double exponential jump diffusion model) to describe the jump asymmetry of time series factors, and prove that DEJD model is more effective than Lee-Carter model in fitting time series factors. In addition, we use the population mortality data predicted by DEJD model to price the SM bonds in Chinese market, providing an important reference for the promotion of SM bond in China.

• article
YANG Xin; LI Bingyue; TIAN Ping
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.001

In this paper, we consider the ultrahigh dimensional partially linear model, in which the dimension of the parametric vector is exponential order of the sample size. Based on profile least squares and regularization after retention method, we propose a new method to perform variable selection for the ultrahigh dimensional partially linear model. Under certain regularity conditions, it is proved that the estimator achieves sign consistency. Compared with Lasso, SIS-Lasso and adaptive Lasso, it is found that the proposed method is better in terms of recovering the coefficient sign of linear part through the numerical simulation and real data analysis.

• article
HU Siyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.002

This paper studies an iterative method of estimating parameters in Gamma distribution based on maximum likelihood estimation and EM algorithm improved by non gradient information spectrum residual method in the case of classified data, Type-I interval censered data, Type-II interval censered data, and it proves the strong consistency of the algorithm. The simulation results show that the iterative method proposed in this paper can greatly shorten the running time while ensuring the accuracy, the estimated mean square error tends to zero with the increase of sample size.

• article
DU Mingyue; SUN Jianguo
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.006

Interval-censored failure time data are a general type of failure time or time-to-event data where the failure time of interest is known or observed only to lie in an interval or window instead of being observed exactly. They often occur in many fields, including demographical studies, epidemiological studies, medical or public health research and social science, and in different forms. A common and general set-up that naturally yields interval-censored data is the study with
longitudinal or periodical follow-ups such as many clinical trials or observation studies. In this paper, after some brief discussion about the background and some commonly used models, we will review some recent advances, mainly during about last five years, on several important topics related to regression analysis as well as some issues that need more research in the analysis of interval-censored data.

• article
CHEN Mu-Fa
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.001

The paper consists of three parts. The first one is from the ergodic theorem of Markov chain to L.K. Hua's fundamental theorem on the optimization of economics. The second one is the Hua's revised version and the author's modification of Hua's theorem. The third one is the computational algorithms on the maximal eigenpair of the structure matrix in the economic system. Some examples are illustrated.

• article
YANG Zhaoqiang; TIAN Yougong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.001

This paper constructs the assets portfolio of lever corporation by the structural approach. Because irreversibility and uncertainty of corporate bankruptcy, the corporate bankruptcy is equivalent to a default of the bonds. By using the parabolic stochastic partial differential equations (SPDE) which the lookback option satisfied,the assets portfolio pricing model of lever corporation is derived under the mixed jump-diffusion fractional Brownian motion (MJD-fBm) environment.
When the lever corporation in the financial crisis, Shareholders use capital injection to make up for operating losses and debt servicing, then the probability of no default before the bonds maturity and the conditional distribution of the lever corporation assets is obtained, and the pricing formula for lookback option is derived. In the end, a numerical example is given to illustrate the influence of different Hurst parameters and risk coefficient and stock asset weight to the default
probability of the lever corporation.

• article
WANG Hao; CHENG Xiaoqiang; GONG Xiaojie
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.007

This article considers the optimal dividend policy with delayed capital injections, and assumes that the capital injection delay follows the exponential distribution. We aim to find the optimal dividend and capital injection strategies to maximize the utility of dividend and capital. Since surplus process of the insurance company involves a mixed Poisson process, we use a stochastic differential equation to characterize the surplus process by adopting diffusion approximation
techniques, and then we obtain the value function under the utility criterion. When the value function is smooth, the quasi variational inequality is obtained by using the dynamic programming principle. In this paper, we consider the value function from three different regions (the dividend area, the continuous area and the capital injection area). Through the boundary conditions, we derive the expression of the value function in different regions and present the verification theorem. A numerical example is presented to illustrate the effects of the capital injection delay under different parameters.

• article
LIN Na;LIU Yuanyuan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.005

In this paper, we investigate algebraic and exponential transience for continuous-time Markov chains (CTMCs). Equivalent relations of these transience are revealed between CTMCs and their jump chains and dual processes. The results are further applied to derive the criteria of these transience for general CTMCs, generalized Markov branching processes and birth-death processes.

• article
ZENG Weijia; ZHANG Riquan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.007

Lasso is a variable selection method commonly used in machine learning, which is suitable for regression problems with sparsity. Distributed computing is an important way to reduce computing time and improve efficiency when large sample sizes or massive amounts of data are stored on different agents. Based on the equivalent optimization model of Lasso model and the idea of alternating stepwise iteration, this paper constructs a distributed algorithm suitable for
Lasso variable selection. And the convergence of the algorithm is also proved. Finally, the distributed algorithm constructed in this paper is compared with cyclic-coordinate descent and ADMM algorithm through numerical experiments. For the sparse regression problem with large sample set, the algorithm proposed in this paper has better advantages in computing time and precision.

• article
JING Haojie; PENG Jiangyan; JIANG Zhiquan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.002

This paper considers a discrete-time risk model with compound dependence. The risk-free and risky investments of an insurer lead to arbitrarily dependent stochastic discount factors. The claim-sizes are assumed to follow a one-sided linear process with pairwise asymptotically independent innovations. The innovations and the stochastic discount factors are mutually independent. We assume that innovations are not necessarily identically distributed nonnegative random variables with distributions F_1,F_2,\cdots,F_n. When the average distribution n^{-1}\tsm_{i=1}^nF_iis heavy-tailed, we establish some asymptotic estimates for the finite-time ruin probabilities of this discrete time risk model. We demonstrate our obtained results through a crude Monte Carlo simulation.

• article
LI Zhi; LI Zhiming
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.003

General minimum lower-order confounding and minimum aberration are two important criteria to select s\,(s\geq 2)-level optimal regular fractional factorial designs. Their classification are based on the aliased component-number and word-length patterns, respectively. The paper mainly studies some properties of the aliased component-number pattern for s-level regular designs. We obtain that the elements of word-length pattern are expressed as some functions of aliased component-numbers under s-level case. It reveals the relationship between the aliased component-number and word-length patterns. On the other hand, we can calculate some aliased component-numbers by word-length pattern. Further, the formulas of some aliased component-numbers are provided for two-level designs.

• article
PAN Qing; ZHAO Xiaobing
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.003

Modeling analysis and reasonable prediction of medical costs are the basis and foundation for the determination of medical insurance costs. High-dimensional additional information in medical costs plays an important role in long-term prediction. This paper proposes a partial linear multi-indicator additive model to fit
and predict longitudinal medical cost data with high-dimensional features and uses two different dimensionality reduction estimation methods to estimate the model and applies the model to a set of high-dimensional dimensions. The longitudinal medical cost data of the variable is used for case analysis.

• article
LUO Xuxiang; LIU Zaiming
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.004

A queueing-inventory system with cancellation, common life time and non-preemptive priority is considered, in which customer arrives according to a Poisson process and service time follows an exponentially distribution. By formulating the system process into a level-dependent quasi-birth-and-death process (LDQBD), the stability condition and steady-state probability vectors under Neuts-Rao truncation method are obtained. Some performance measures and expected cost function are also given. Then, the optimal maximum inventory level and minimum cost are achieved through numerical simulations. Finally, the sensitivities analysis on major parameters are performed to provide more managerial insights.

• article
LI Feng;LIU Xin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.003

This paper discusses the optimal design problem for the hierarchical linear model with intraclass positive correlation. A-optimal designs are considered for the estimation of the fixed effects as well as the prediction of random effects. We provide two equivalence theorems to determine the $A$-optimality of a given design. Two illustrative examples of the A-optimal designs are presented.

• article
LIN Xiang; QIAN Yiping; SHU Yingbin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.005

In this paper we investigate a continuous-time optimal portfolio selection problem for a risk-averse investor based on a relative log-return. Investor can invest her wealth in a risk-free asset and a risky stock. The objective of the investor is to exceed the performance of a stochastic benchmark that is not perfectly correlated
with the risky stock. Investor chooses a dynamic portfolio strategy in order to maximize her expected terminal utility of the weight sum of absolute log-return and relative log-return. By using the dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman equation of the optimal portfolio strategy and the value function is established. Furthermore, closed-form expressions of the optimal portfolio strategy and the value function under the investor with a exponential utility function are derived. The effect of the relative return on the optimal portfolio strategy is also analyzed. The result shows that the relative return works against a investor's intrinsic risk-taking tendency. Finally, numerical examples are provided to illustrate how the optimal portfolio strategy and the value function change when some model parameters vary.

• article
WANG Jing; YAN Yanyan; ZHANG Yuhui
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.007

In this summary report, we introduce some basic theory of single birth processes as the supplement of \ncite{1}, including the probabilistic meaning of some numerical characteristics, the distributions and moments of the integral-type functional of single birth processes, as well as the distributions of the staying
times, the first hitting time and the last exit times etc.

• article
ZHU Ke;JIANG Yingkai;WANG Xiang;SHI Zhicheng;YANG Chao;LIU Hanzhong;DENG Ke
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.007

With the deep development of the economic society,and the remarkable rise in people's living standards, customer requirements are becoming more and more intense. Meanwhile, the rapid development of the Internet technology and smart manufacturing has provided a solid industrial foundation for meeting such needs. Customized production has gradually become an important production mode. Different from traditional massive production, in a customized production mode, a product often consists of multiple customized modules, generating thousands of customized combinations, and usually a small number of products will be produced for each combination. Taking certification cost into account, the customized production makes the traditional product certification procedure unrealistic because we can not authenticate several prototypes for each customized combination. Therefore, there is an urgent requirement for developing theories and methods of customized product certification, which can accurately assess the quality of customized products at an acceptable certification cost. In this article, we propose a general framework for customized product certification based on certification big data and statistical models and illustrate it on
refrigerator safety certification. This framework transforms the safety certification of customized products into the assessment of product safety risks, establishes a quantitative statistical model to characterize the risks, and uses the principles and methods of experimental design to develop economical certification schemes. Our certification big data based simulation results indicate that this framework has the potential to achieve reliable, efficient, and intelligent customized product certification, which has important theoretical and practical significance for certification mode innovation.

• article
WU Xiao; GUO Zhenbin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.06.004

In this paper, we study the convergence problem of a sequence of first passage Markov decision processes with constraints and varying discount factors. Using the occupation measures'' and its related properties, we transform the constrained optimality problems into linear programming problems on the set of occupation measures (i.e., the convex analytic approach), and then prove that the optimal values and optimal policies of the original first passage Markov decision processes converge respectively to those of the limit'' one.

• article
HONG Hejing; HU Zechun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.011

Let \mu_n be the standard Gaussian measure on \mathbb{R}^n and X be a random vector on \mathbb{R}^n with the law \mu_n. U-conjecture states that if f and g are two polynomials on \mathbb{R}^n such that f(X) and g(X) are independent, then there exist an orthogonal transformation Y=LX on \mathbb{R}^n and an integer k such that f\circ L^{-1} is a function of (y_1,y_2,\cdots,y_k) and g\circ L^{-1} is a function of (y_{k+1},y_{k+2},\cdots,y_n). In this case, f and g are said to be unlinked. In this note, we prove that two symmetric, quasi-convex polynomials f and g are unlinked if f(X) and g(X) are independent.

• article
ZHANG Longteng; CHEN Jin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.006

In this paper, we present explicit sufficient and necessary conditions for the compactness of the semigroups associated with time change of non-local Dirichlet forms, whose jumping kernels have finite second moment.

• article
TIAN Dejian; FANG Jie
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.006

The paper investigates the optimal consumption and portfolio with consistence performance under Knightian uncertainty. The agent has Knightian uncertainty for the expected return of risky asset, which is characterized by \kappa-ignorance model. Consistent performance model asks for a dynamic wealth constraint, which requires the wealth always stays at or above the weighted average of the entire historical wealth levels. In the infinite time horizon, we obtain the
optimal consumption and portfolio explicit solution for the model by the HJB equation and verification theorem.

• article
ZHANG Bo;ZHANG Zhimin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.009

In this paper, we use the complex fourier series expansion method (CFS) to price guaranteed minimum death benefits (GMDB). The main idea is to expand the Fourier series of the auxiliary function. The density function of remaining lifetime has two forms in this paper, namely combination-of-exponentials density and piecewise constant forces of mortality assumption, and the coefficients of series are estimated by using the known characteristic function of the general L\'{e}vy model. We mainly consider the value of GMDB products under call options and put options. In the numerical experiment section, we also demonstrate the
advantages of CFS in calculation accuracy and running time by comparing with cosine series expansion method (COS) and Monte Carlo method (MC).

• article
FU Zongkui; FEI Dandan; ZHANG Cong; SUN Limin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.008

In this paper, using the property of NSD random variable sequence, moment inequality and three series theorem, we obtain complete convergence for NSD random variables sequences under certain moment conditions. The results generalize the results of independent sequences for Chow and Lai\ucite{15,16} and Jajte\ucite{17}.

• article
CHEN Minqiong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.004

This article proposes a new consistent nonparametric test of the hypothesis that a random vector is symmetrically distributed given another random vector. The test is based on the weighted integral of the discrepancy between two empirical characteristic functions. By choosing a special weighted function, we obtain a simple form of the test statistic, which is the form of a $V$-\,statistic. Using the theory of $V$-\,statistic, we derive the asymptotical properties of the test. Simulation results show that our test is slightly affected by the dimension of the conditional vector and often still possess high power when the conditional vector has no finite moments. We also illustrate the power effectiveness of our test in the analysis of a real dataset.

• article
RONG Guocai; WANG Yanan; WEI Chengdong; DENG Lifeng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.003

In actual data, especially medical data, the covariates are contaminated or interfered by certain factors, while the real covariates cannot be observed. This paper discusses how to adjust the disturbed covariates in the proportional risk model. Covariate existed in the adjustment methods cannot be directly used for survival
data, in order to solve this problem, we use kernel functions to construct the interference factors of the distribution function, the interference of covariate smoothly get the estimate of the real covariate, again to get the parameters in the model of regression estimate, and completed the estimate satisfying consistency and asymptotic normality. We also proposed the use of Minorization-Maximization (MM) algorithm to obtain parameter estimates. The first M is to construct a surrogate function by the convexity of the exponential function and the negative logarithm function, which the Hessian matrix is a diagonal matrix; The second M is to obtain the estimators by maximizing the surrogate function. Finally, we demonstrate the feasibility of our proposed method through numerical simulation and real data research.

• article
ZHANG Yingying; RONG Tengzhong; LI Manman
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.004

Prospective phase II trials usually result in failures in phase III trials. For randomized controlled phase II and phase III trials which are conducted with patients randomized to one of two treatments where the variances of the normally distributed responses are assumed to be known, we analytically obtain the estimated
and theoretical assurances for the three cases (no, additive, and multiplicative bias adjustments). Under some minor assumptions, we show that the estimated assurances for the three cases are increasing functions of the per group number of patients and the observed treatment effect of the phase II trial, respectively; and for Case 3, the estimated assurance is an increasing function of the retention factor. When the true treatment effect of phase III is assumed to be a known constant, we show that the theoretical assurances for the three cases are constants which are equal to the designed power or one minus the type II error. Moreover, we show that the estimated assurances are always less than the theoretical assurance. We also obtain the analytical formulas of the probabilities of launching a phase III study for the three cases. Moreover, for Case 3, we show that the probability of launching a phase III study is an increasing function of the retention factor. According to our theoretical investigations, we find that the true treatment effect of phase III has no effect in the simulations. Finally, the simulations are conducted to illustrate the theoretical investigations.

• article
CHENG Tian; XIA Zhiming
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.008

This paper studies the statistical inference and algorithm design problems in the mixture model with change point. For multi-classified mixture data with change point, this paper designs an improved EM algorithm based on the maximum likelihood estimation of parameters, and proves the large sample nature of the change point estimator and the mixture parameter estimator. In order to verify the effectiveness of the method, we conducted some simulation experiments.
The results show that the EM algorithm that does not consider the change point has a poor estimate on the classification result, and even loses some categories; Our improved EM algorithm can accurately locate the location of the change point, and at the same time obtain accurate estimates for the corresponding parameters of each category.

• article
HAN Qi;LU Ziqiang;HAN Yanan;CHEN Zhihe
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.006

We study discrete-time quantum random walks on the $N$-ary tree by a framework for discrete-time quantum random walks, this framework has no need for coin spaces, it just choose the evolution operator with no constraints other than unitarity, and contain path enumeration using regeneration structures and $z$ transform. As a result, we calculate the generating function of the amplitude at the root in closed form.

• article
DENG Yong; HU Yijun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.01.005

In this paper, we introduce three new classes of multivariate risk statistics, named multivariate comonotonic quasiconvex risk statistics, multivariate quasiconvex risk statistics and multivariate empirical-law-invariant quasiconvex risk statistics, respectively. Representation results for them are provided by dual method. The results of this paper is not only the generalization of one-dimensional quasiconvex risk statistics, but also the extension of multivariate convex risk statistics.

• article
WU Jie;XU Zhonghao;ZHAI Xintong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.04.008

COVID-19 has caused huge impact to financial system, among which stock market is one of the main sources of infection. This paper investigates stock market volatility based on complex networks, proposing the method of applying articulation point-targeted attack (APTA) in the model of the stock market volatility. The strategy of APTA is removing the most destructive articulation points (AP) that will result in most nodes disconnected from the giant connected component (GCC) by iterating, and eventually uncovering the residual giant bicomponent (RGB) that maintains the structural stability of the network. This paper models
stock network based on realized volatility and thresholds, separates research period into steady-developing period and risk-fluctuating period, compares and analyzes the topological properties. Network centrality indexes and APTA are used to discover the important stocks that need to be supervised specially, thus avoiding the big-scale spread of risks or concurrent risks, and helping the supervisors maintain financial stability.

• article
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST.
• article
QIU Chunjuan; GAO Shuhui; QIAN Linyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.01.010

The modes of piecewise and the number of intervalsare particularly important in the formulation of compensation scheme for critical illness insurance in China. In this paper, under the three subsection modes of interval bisection, constant ratio increment and constant ratio decrement, the theoretical models are established with interval quantity as independent variable and serious illness insurance compensation amount as dependent variable. Taking the expected compensation ratio as the standard to measure the compensation level of serious illness insurance, we can get the following results: first, the optimal number of
intervals corresponding to the three interval modes are respectively: 3, 3 and 5; second, under the setting of the number of piecewise, the compensation level of the interval equal proportion increasing mode is the highest, the interval equal proportion decreasing mode is the second, and the compensation level of the interval equal proportion increasing mode is the lowest, But there is little difference between the three. Then, based on the data of CHARLS in 2015, we calculated the incidence of family catastrophic medical expenditure under the three interval modes as 7.13%, 7.26% and 7.69% respectively. The result is consistent with that of the theory.

• article
YANG Chaoran; CHANG Guangping
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.002

{Many tests have been developed to check the normality assumption. These tests are mainly defined in two types: one is empirical distribution function test, the other is correlation and regression test. In this paper, we propose a new two-step test method based on the L_2 Wasserstein distance and the approximate distribution of i th sample order statistic. We discuss the properties of the new test method under the null hypothesis, and compare the power with other most commonly tests for four alternative groups. Finally, the new method is applied to analyse the real problem. The simulation results show that the new test
method improves the efficiency in identifying asymmetric long-tailed alternatives.

• article
ZHOU Niwen; CHEN Feifei
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.005

When the response variables are missing randomly, in the process of statistical inference of the parameters of interest, two common working models are the regression function model and the selection probability model. In order to avoid the inference bias caused by the model setting error, the regression function model and selection probability models are necessary and meaningful for model testing. For this reason, for the first time in this paper, the feature functions are applied to the model testing problem of random missing response variables and discrete variable response variables, and a Euclidean distance between sample points is constructed based on test statistic. The proposed test avoids the selection of smoothing parameters such as bandwidth, and at the same time can detect the local alternative hypothesis at the fastest parameter speed. Further, this paper aims at the composite null hypothesis: at least one of the two working models is designed. It is correct, and a test method of the merged model is proposed. An important application scenario of this test is to determine whether the bistable estimation of the parameter is a coincident estimate. This article deeply studies the test of the merged model in the original hypothesis, the global alternative hypothesis, and the local alternative hypothesis. The asymptotic property of the following, and using the boostrap method to determine the rejection domain of the test, study the performance of the merge model test under a limited sample. Finally, this article applies the proposed merge model test method to
analyze the clinical research of AIDS research Test Data. It is worth mentioning that the combined model test mentioned in this article not only has good performance, but also the method is simple and easy to implement, and the corresponding p-value is easy to calculate.

• article
DING Jianhua; ZHANG Hongyu; ZHANG Zhiqiang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.009

Assuming the observations are imprecise and modeling the observations by uncertain variables, this paper proposes statistical inferences for uncertain semiparametric regression model when nonparametric function is subject to monotonicity constraint. Monotonic Bernstein polynomials are used to approximate the nonparametric function and quadratic programming algorithm is used to compute the estimate. A numerical example is given to illustrate the proposed methods.

• article
XU Hao; WEI Zhiya; PENG Xuhui
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.03.002

This paper investigates a bidimensional risk model with interference, in which the vectors of claim process and premium process are both compound Poisson-Geometric processes. Through martingale method and stopping time technique, we get the upper bound of the ruin probability. When the marginal of claim vector and premium vector follow bivariate FGM (Farlic-Gumbel-Morgenstern) class, we have discussed some properties of the upper bound.

• article
LI Guanghui; LI Junpeng; ZHANG Chongqi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.006

It is difficult to prove the optimality of a mixture design in the region with complex constraints, however, it is relatively easy to negate the optimality of the design. In this paper, we construct a set of dense lattice points in the experimental region with complex constraint. It can not only be used to evaluate the optimization
of a design, but also to compare the advantages of multiple local optimal designs. As an alternative set of points, the densely covered set of lattice points can produce the local optimal design in the constrained region. This method is effective through case analysis.

• article
SUN Lei; ZHU Yuyu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2022.02.008

This paper analyzes the risk spillover effects of the stock market on commercial banks from a new perspective. First, we use the Granger causality test to verify the relationship between the stock market and the commercial banks. Then, we use the CoVaR model based on quantile regressions to calculate the risk spillover effects of the stock market to commercial banks. Although the risk level of the state-owned banks is relatively minimal, the banks experience the largest risk spillover effects in the stock market. The risk spillover effects of the stock market to the city commercial banks are in the middle, while the overall systematic
risk impacts of the stock market on the joint-stock banks are small. In addition, the sensitivity of the state-owned banks, joint-stock banks, and city commercial banks to the stock market increased gradually. The results of this paper have important policy implications for weakening the impacts of the stock market on commercial banks, and reducing external risks on commercial banks.