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• article
MA Jian
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.04.006

Variable selection is of significant importance for classification and regression tasks in machine learning and statistical applications where both predictability and explainability are needed. In this paper, a Copula Entropy (CE) based method for variable selection which use CE based ranks to select variables is proposed. The method is both model-free and tuning-free. Comparison experiments between the proposed method and traditional variable selection methods, such as distance correlation, Hilbert-Schmidt independence criterion, stepwise selection, regularized generalized linear models and adaptive LASSO, were conducted on
the UCI heart disease data. Experimental results show that CE based method can select the right' variables out more effectively and derive better interpretable results than traditional methods do without sacrificing accuracy performance. It is believed that CE based variable selection can help to build more explainable models.

• article
NIU Yong; LI Huapeng; LIU Yanghui; XIONG Shifeng; YU Zhou; ZHANG Riquan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.01.007

With the improvement of data collection and storage capacity, ultra-high dimensional data\ucite{9}, that is, dimensionality with the exponential growth of samples appears in many scientific neighborhoods. At this time, penalized variable selection methods generally encounter three  challenges: computational expediency, statistical accuracy, and algorithmic stability, which are limited in handling ultra-high dimensional problems. Fan and Lv\ucite{9} proposed the method of ultra-high dimensional feature screening, and achieved a lot of research results in the past ten years, which has become the most popular field of research in statistics. This paper mainly introduces the related work of ultra-high dimensional screening method from four aspects: the screening methods with model hypothesis, including parametric, non-parametric and semi-parametric model hypothesis, model-free hypothesis, and screening methods for special data. Finally, we briefly discuss the existing problems of ultra-high dimensional screening methods and some future directions.

• article
SUN Jiajing；MCCABE Brendan；CUI Wenquan；LI Guoxing
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.00.001

The traditional PAR process (Poisson autoregressive process) assumes that the arrival process is the equi-dispersed Poisson process, with its mean being equal to its variance. Whereas the arrival process in the real DGP (data generating process) could either be over-dispersed, with variance being greater than the mean, or under-dispersed, with variance being less than the mean. This paper proposes using the Katz family distributions to model the arrival process in the INAR process (integer valued autoregressive process with Katz arrivals) and deploying Monte Carlo simulations to examine the performance of maximum likelihood (ML) and method of moments (MM) estimators of INAR-Katz model. Finally, we used the INAR-Katz process to model count data of hospital emergency room visits for respiratory disease. The results show that the INAR-Katz model outperforms the Poisson model, PAR(1) model, and has great potential in empirical application.

• article
QI Kai; YANG Hu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.03.001

Index tracking mainly focuses on replicating or tracking the performance of a financial index which is also a popular passive portfolio management strategy. The classical methods often considerthe full replication consisted of all asserts of an index. However, the full replication often suffers from small and illiquid positions and high cost as the number of asserts increasing. Thus, the investors intend to purchase sparse portfolios. In stock markets, besides, there are still apparently existing group effects among stocks. This paper proposes the nonnegative sparse group lasso method for model selection and estimation to grouped variables without overlapping. We provide almost necessary and sufficient conditions for the variable selection and estimation consistency of the method in finite dimensional group cases. To get the solutions of the model, we derive a computational method based on coordinate decent algorithm. To track the index, the nonnegative sparse group lasso outperforms other current methods with group effects such as nonnegativeelastic net, according to tracking error.

• 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
GUO Yongjiang; ZHANG Yuyan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.01.001

We obtain the strong approximation of the sojourn time progress for a two-stage tandem queue in heavy traffic, that is, the traffic intensity $\rho_1=\rho_2=1$. The sojourn time is the period from a customer's arrival to her departure, and the strong approximation is a function of Brownian motion.

• 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
LIU Tingting; YANG Lianqiang;WANG Xuejun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.004

Modal regression based on nonparametric quantile estimator is given. Unlike the traditional mean and median regression, modal regression uses mode but not mean or median to represent the center of a conditional distribution, which helps the model to be more robust for outliers, asymmetric or heavy-tailed distribution. Most of solutions for modal regression are based on kernel estimation of density. This paper studies a new solution for modal regression by means of nonparametric quantile estimator. This method builds on the fact that the distribution function is the inverse of the quantile function, then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function. The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation.

• WANG Dan; PI Lin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.02.001

This paper establishes a empirical likelihood method to detect change-point in the mean of heavy-tailed sequence. Firstly, under the null and the alternative hypothesis, the empirical likelihood functions are obtained in the heavy-tailed observations. Secondly, the empirical likelihood ratio statistics is constructed based on empirical likelihood functions. And under the null hypothesis, the asymptotic distribution of statistics is given. Finally, Monte Carlo simulation is carried out to verify the correctness of the method. The simulation results show that the performance of our method is well to detect mean change in heavy-tailed sequence.

• article
PANG Yingying；CHEN Zhenlong；ZHENG Changmei；ZHANG Qiaoyan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.001

The existing statistics in unit root tests of ESTAR-GARCH model often need to calculate the variance of specimen. In this paper, the empirical likelihood ratio statistics are proposed to deduce the limiting distribution of them, so that the random errors caused by variance calculation are avoided. And then, a critical value of the statistics can be received through simulation, the power of the QML test and the empirical likelihood ratio statistics has been compared and
studied. Monte Carlo simulation shows that compared with the QML test, the power and the criterion of tests is more fruitful and more scientific, through the empirical likelihood ratio statistics. Avoiding the random errors of the calculation of variance, the accuracy of tests is clearly increased by using the empirical likelihood ratio statistics. Finally, the empirical study of SSE can further illustrate the higher test efficiency of this statistic.

• article
LONG Wei; LI Yanting
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.03.001

Multiple discrete data are very common in the manufacturing industry. Most control charts are built based on the assumption of the multivariate Poisson model with a single common covariance term, which allows only equal covariance. However, this assumption may not be realistic, for the cases observed in different
regions sometimes are dependent with different covariance. Besides, these control charts cannot provide fault diagnosis information. This article presents GMP-CUSUM chart based on the multivariate Poisson model with two-way covariance structure. Using Monte Carlo simulation, we compare the average running chain length (ARL) of traditional MP control chart and the new control chart considering various factors. The results show that the latter model is more suitable for modeling multivariate discrete data and the new control chart increases sensitivity to process shifts. When applied to raw data directly, the proposed method is powerful yet simple to use in practice.

• article
XIONG Wenjie; ZHANG Zhengchen
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.02.004

Coherent systems are very important in reliability,survival analysis and other life sciences. In this paper, we consider the number of working components in an $(n-k+1)$-out-of-$n$ system, given that at least $(n-m+1)$ components are working at time $t$, and the system has failed at time $t$. In this condition, we compute the probability that there are exactly $i$ working components. First the reliability and several stochastic properties are obtained. Furthermore, we extend the results to general coherent systems with absolutely continuous and exchangeable components.

• article
ZHU Jiaqing; ZHAO Shengli
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.01.001

Order of addition designs with conditions are widely used in experiments, but references on this subject are rather primitive. The paper gives the definition of conditional main effect of pair-wise ordering factor, studies the orthogonality of conditional main effects of pair-wise ordering factors, and proposes the model of order of addition designs with conditions. Finally, it gives the methods for data analysis through two examples.

• article
YANG Yiping;YU Lu;WU Dongsheng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.02.001

Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample
properties of the proposed method are studied by a simulation study, and a real example is analyzed.

• article
CAO Ping; XIA Zhiming
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.005

When the sample size is $N$, the computational complexity of the least squares estimate of mean change point is O(N^2), and it's necessary to reduce the computational complexity in the case of huge data. In this paper, a two-stage fast scanning algorithm is proposed for the estimation of mean change point, and it is proved that this method has the same convergence speed and limiting distribution as the least squares estimation of mean change point, and the optimal complexity of the new algorithm is O(N^{4/3}\cdot b_n^{2/3}). We have conducted sufficient data experiments in terms of computation time and estimated efficiency, and the results show that the estimated efficiency of the new and old methods is similar, but the computation time of our method is obviously shortened.

• HU Danqing; GU Yongquan; ZHAO Weihua
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.004

When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.

• article
LIANG Longyue; SHI Haihua
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.01.002

This paper establishes limsup type law of the iterated logarithm of the occupation measure, using the asymptotic equivalence relation between the occupation measure and the number of excursion process of a symmetric Cauchy process. Furthermore, by using the density theorem and the economic coverage method, it derives the exact Hausdorff measure for the range of a symmetric Cauchy process in \mathbb{R}.

• article
CUI Jiarong; ZHU Fengyi; LIU Jiamin; XU Wangli
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.01.004

Kolmogorov-Smirnov (KS), Cramer-von Mises (CM) and Anderson-Darling (AD) test, which are based on empirical distribution function (EDF), are well-known statistics in testing univariate normality. In this paper, we focus on the high dimensional case and propose a family of generalized EDF based statistics to test the high-dimensional normal distribution by reducing the dimension of the variable. Not only can we approximate the corresponding critical values of three statistics by Monte Carlo method, we also can investigate the approximate distributions of proposed statistics based on approximate formulas in univariate case under null hypothesis. The Monte Carlo simulation is carried out to demonstrate that the performance of proposed statistics is more competitive than existing methods under some alternative hypotheses. Finally, the proposed tests are applied to real data to illustrate their utility.

• article
CHEN Mu-Fa
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.01.007

This paper is based on Pao-Lu Hsu's lecture'' (2019/3/22) at Peking University and the subsequent expansion of his reports. It begins with some recollections benefited of the author from Professor Hsu, and ends with thanking to a group of professors at Peking University for their support and help over the past decades. The middle part is the theme of the talk. It gives first an overview of personal cross research. Then, from a challenge of computing, the author reports on the study looking for a larger class of complex matrices which have real spectrum. This was done mainly in the last year. It involves the fields of computation, probability, statistical mechanics and quantum mechanics Next, the paper introduces the latest development of algorithms, which is another illustration of the intersection between probability theory and computational mathematics. As the end, it also outlines the understanding of the cross study.

• 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.

• CHEN Xiaoping; LIN Huonan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.001

The lower Hausdorff dimension results for the range and the graph of multi-parameter operator stable L\'{e}vy processes are established. The consequences are completely determined by the eigenvalues of its exponent matrix.

• DU Mengying; WEN Limin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.002

estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample
size is small.

• article
LI Doudou; ZHANG Mei
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.04.001

We consider a critical branching process with $\psi$-mixing immigration and prove a functional limit theorem, improving the results in previous literatures. As applications, we obtain central limit theorems for an estimator of the offspring mean.

• article
WANG Lingdi； REN Panpan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.002

In this paper, we discuss the exponential ergodicity of Markov switching diffusion processes, presenting criteria of f-exponential ergodicity for the processes with reflecting boundary at origin. When the one-dimensional diffusion processes are stochastically ordered for any fixed environment, the explicit estimates of the exponential ergodic rate for the process are investigated by means of the coupling method.

• article
LIU Weiqiang; ZHAN Mengya
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.06.006

The paper considers the optimal dividend and capital injection strategies for the compound poisson risk process in a random interest rates environment. In the model, the surplus is assumed to be ordinary but the interest rates are governed by an exogenous Markov chain. Here, the problem is solved by two steps. First, we find out the capital injection form that the optimal strategy should follow. Then we look for the optimal solution in the restricted set with the particular capital injection form. In the paper, we discuss restricted'' and unrestricted'' two cases and provide a possible solution for `unrestricted'' case when the claim distribution is exponential.

• article
YE Chuanxiu; ZHAO Yongxia
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.01.006

In this paper, we consider the optimal dividend problem in the spectrally positive L\'{e}vy model with regime switching. By an auxiliary optimal problem, the principle of dynamic programming and the fluctuation theory of L\'{e}vy processes, we show that optimal strategy is a modulated barrier strategy. The value function and the optimal dividend barrier are obtained by iteration.

• CHEN Ranran; LI Gaorong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.006

In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data.

• article
LING Xiaoliang; GAO Yu; LI Ping
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.05.001

In reliability engineering, components of the coherent system may be dependent since they operate in a common random environment. This paper uses multivariate distortion function to describe the dependence among lifetimes of components and the structure function of the coherent system. Some sufficient conditions are given to compare two coherent systems under different random environments in the sense of usual stochastic order, failure rate order, reversed failure rate order and likelihood ratio order.

• article
SONG Yanan; ZHAO Xuejing
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.02.003

The requirements of model accuracy and robustness make the outlier detection and robust estimation become more and more important in the model construction. In this paper, we first use the high-dimensional influential measure (HIM) based on the marginal correlation and the high-dimensional discriminant method based on the distance correlation (HDC) to respectively detect the outliers in the data set. Then the points are divided into two parts: normal points and abnormal points. Based on the initial normal point set, we construct the method of recovery for the points that are misclassified to normal point set, by using a kind of robust coefficient estimation method and the concept of hyper ellipsoid contour in residual space. Thereafter the outlier probability of each point in the abnormal point set are calculated to further recover the normal points that are misspecified in the abnormal point set and thus detect the true outlier value. The accuracy rate of outlier detection has been further improved. The performance of the proposed method is illustrated through simulations of three types of anomaly data under two predictive data structures, as well as three real examples.

• ZHANG Yingying; RONG Tengzhong; LI Manman
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.005

We prove three theorems for iid discrete randomvariables taking two values, three values, and k (3\leq k<\infty) valuesby using the technique of indicator function. Under some specifications of the probabilities, we prove that the sum is a minimal sufficient statistics for the unknown parameter of interest of the discrete random variable taking two values, three values, and k (3\leq k<\infty) values. For the dice example, a figure shows that the specifications of the six probabilities are between 0 and 1 and sum to 1, and a fair dice is possible.

• article
ZHAO Xia；SHI Yu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.008

This paper studies the optimal asset allocation and reinsurance problem under mean-variance-CVaR criteria for an insurer in continuous-time. We obtain the closed-form solution of optimization problem by using martingale method. Numerical results show the trends of optimal wealth, investment and reinsurance strategies with various parameter values.

• DING Feipeng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.003

This paper constructs a penalized empirical likelihood estimation method via quadratic inference function method, filter method and empirical likelihood estimation method. Under some regular conditions, we derived the large sample properties of estimators and show that the proposed empirical likelihood ratio is asymptotically to chi-square distribution. Furthermore, the infinite sample performance of the proposed method is evaluated by Monte Carlo simulation and real
data analysis.

• article
ZHANG Chi; TIAN Guoliang; LIU Yin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.03.006

In fields of sociology, psychology, ecology, insurance, medicine and epidemiology, count data are often collected for specific studies. While count data without zero-category or with excess zeros arise quite frequently, a series of zero-truncated and zero-inflated models were soon developed to analyze these kinds of data, such as zero-truncated/inflated Poisson distribution and zero-truncated/inflated negative binomial distribution. It is necessary to make statistical inferences on unknown parameters when fitting data by these models. Existing studies merely focus on one of these models. In this paper, based on the stochastic representations of zero-truncated and zero-inflated distributions proposed in recent years, we construct a general method to obtain the maximum likelihood estimates of parameters under a unified framework, and make a review on familiar discrete distributions. Moreover, zero-adjusted models are further proposed to extend the applications, aiming to provide researchers appropriate and convenient methods in count data analyses. All methods are demonstrated by simulation studies and two real data analyses.

• article
LI Qi; ZHANG Jiujun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.03.002

In this paper, we propose distribution-free mixed exponentially weighted moving average-cumulative sum (EWMA-CUSUM) and mixed cumulative sum -- exponentially weighted moving average (CUSUM-EWMA) control charts based on the Ansari-Bradley test for detecting process scale without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured in terms of average run-length and some other performance indexes. The effect of sample size in phase I and phase II on phase II of the proposed charts is also investigated. The application of the new chart is illustrated by real data examples.

• article
YUAN Shoucheng; ZHOU Jie; SHEN Jieqiong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.04.003

In this article we study test of sphericity for high-dimensional covariance matrix in the general population based on random matrix theory. When the sample size is less than data dimension, the classical likelihood ratio test has poor performance for test of sphericity. Thus, we propose a new statistic for test of sphericity by
using the higher moments of spectral distribution of the sample covariance matrix, and derive the asymptotic distribution of the statistic under the null hypothesis. Simulation results show that the proposed statistics can effectively improve the power of the test of sphericity for high dimensional data, and have especially significant effects for Spiked model, on the basis of controlling the type-one error probability.

• article
XIA Xiaoyu; YAN Litan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2021.02.002

Let B^H=\{B_t^H,\,0\leq t\leq T\}$be a fractional Brownian motion with Hurst index H\in(0,1/2)\cup(1/2,1) and let b be a Borel measurable function such that |b(t,x)|\leq(1+|x|)f(t)$ for x\in\mathbb{R}$and$0<t<T$, where$f$is a non-negative Borel function. In this note, we consider the existence of a weak solution for the stochastic differential equation of the form $X_t=x+B_t^H+\int_0^tb(s,X_s)\md s.$ It is important to note that$f\$ can be unbounded such as f(t)=(T-t)^{-\beta} and f(t)=t^{-\alpha} for some 0<\alpha,\beta<1. This question is not trivial for stochastic differential equations driven by fractional Brownian motion.

• SONG Zhi; LIU Yanchun; TAO Guihong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2019.06.007

A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some
percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.

• article
WU Yanhua；SHI Yufeng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.05.003

Since the jump of an asset price has a strong effect on the estimate and forecast volatility, it has received widespread attention. Following HAR-CJ model introduced by Andersen et al, lots of works focus on this problem. In this paper, through a threshold technique, we distinguish the true and false jumps. Then we introduce two models, HAR-CTFJ model and LHAR-CTFJ model. Our result shows that the effect from the true jumps is significant while that from the false jumps is not. Moreover, the SPA test shows that our models (i.e. HAR-CTJ and LHAR-CTJ) are better than the classical HAR-CJ model in the prediction of volatility.

• article
ZHANG Fengyue; WANG Lichun
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. https://doi.org/10.3969/j.issn.1001-4268.2020.03.003

We employ a linear Bayes procedure to estimate the unknown parameter of the uniform distribution R(-\theta,\theta) and propose a linear approximate Bayes estimator (LABE) for \theta, which has a closed analytic solution form and is convenient to use. Numerical simulations indicate that the proposed LABE is close to the ordinary Bayes estimator (BE), which is calculated by numerical integration and the so-called brute-force method as well. Furthermore, we compare the proposed LABE with the Lindley's approximation. The superiorities of the LABE over the classical estimators are also established in terms of the mean squared
error (MSE) criterion.

• 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.