26 February 2024, Volume 40 Issue 1
    

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  • Numerical Simulation of Statistical Behavior for Fractional Cox-Ingersoll-Ross Process#br#
    LIU Bowen, ZHANG Jing, CHEN Xiaopeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 1-17. https://doi.org/10.3969/j.issn.1001-4268.2024.01.001
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Cox-Ingersoll-Ross (CIR) process is an important tool to study stochastic interest rate and stochastic volatility in financial market. The statistical behavior of fractional CIR process is mainly simulated and discussed in this paper. Since there is no analytical expression of the CIR process, two different functions wfbm and fbmld are used to simulate the fractional Brownian motion, and the Euler-Maruyama (EM) method is used to investigate the expectation and variance of the fractional CIR process. Because the distribution of fractional CIR process can not be expressed by the solution of Fokker-Planck equation, the empirical distribution of fractional CIR process is simulated, and the change of empirical distribution with time is obtained. In order to further verify the algorithm and compare the advantages of the two different algorithms, a backward Euler type scheme of the CIR model and the fractional Ornstein-Uhlenbeck (OU) model with analytical solution is carried out. By comparing figure and table, it is found that simulation by the function fbmld have a very high fitting precision with the theoretical analytical solution with expectation and variance.
  • Approximate Bayesian Estimation of the Parameters of Laplace Distribution#br#
    YANG Yanjiao, WANG Lichun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 18-32. https://doi.org/10.3969/j.issn.1001-4268.2024.01.002
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    The Laplacian distribution is one of the most important distributions used to characterize the peak and thick-tailed data. This paper proposes a linear approximation Bayesian estimation with explicit solutions for the two parameters of the Laplace distribution. The superiority of linear approximate Bayesian estimation over other estimators is verified by theoretical derivation and numerical simulations, and the asymptotic behavior of the linear estimation with the increase of sample size is investigated.
  • The M-Estimation for Multiplicative Regression Models with a Diverging Number of Covariates#br#
    FAN Ruiya, ZHANG Shuguang, WU Yaohua
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 33-49. https://doi.org/10.3969/j.issn.1001-4268.2024.01.003
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    In this article, we propose a nonconcave penalized M-estimation of least product relative error (penalized M-LPRE) method for
    multiplicative regression models whose dimension of parameters is sparse and can increase with the sample size. Under some mild conditions, consistency and asymptotic normality of the penalized M-LPRE estimator are established. Numerical simulations and a real data analysis on the body fat are carried out to assess the performance of the proposed method.
  • Varying-Coefficient Model and Applications for the Periodic Time Series#br#
    FANG Xueli, WANG Shouxia
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 50-74. https://doi.org/10.3969/j.issn.1001-4268.2024.01.004
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    The time series in various kinds of fields not only exist a period but also easily affected by external variables of which the effect may vary with time. Sometimes, the period of some time series may be unknown. For the time series with unknown period and affected by external variables, we use a periodic varying-coefficient model to model it. We write the classical decomposition time series model as a partial linear varying-coefficient model with an unknown parameter. Then we approximate the varying-coefficient functions with B-spline and obtain the estimators of the period as well as the periodic sequence and the varying-coefficient functions in the decomposition model. The asymptotic behaviors of the estimators are given in our paper, including the consistency of period estimation and the asymptotic behavior of estimated periodic sequence and the varying-coefficient functions. We illustrate the superiority of our method through simulation studies in Section 4 and the applications to three real data examples including the number of the tourists in Hongkong and Macao and the crude oil price data in Section 5 show the utility of our method.
  • Variable Selection for Functional Additive Models and an Application to the Population Age Structure Data#br#
    CHEN Zhengyu, WANG Xinyi, FENG Zhenghui
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 75-91. https://doi.org/10.3969/j.issn.1001-4268.2024.01.005
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, we study component selection and estimation for functional additive models, which involve a scalar response and a functional predictor. Three methods are proposed to achieve a much more parsimonious model structure with better interpretation. Based on a cross-sectional data of 82 economics in 2018, we build a non-life insurance demand model with age proportion log hazard curve of the population as functional independent variable. We found that the declining demographic structure and higher proportion of people who heading for retirement has negative impact on non-life insurance demand.
  • Empirical Likelihood Testing for Memory Parameter in Gaussian and Non-Gaussion Stationary Time Series#br#
    ZHANG Xiuzhen, LU Zhiping
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 98-106. https://doi.org/10.3969/j.issn.1001-4268.2024.01.006
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    In this paper, we apply empirical likelihood for testing the significance of long memory parameter in Gaussian and non-Gaussian stationary model. We start from the wide-used long memory model (ARFIMA) to derive the empirical likelihood ratio statistics of memory parameter. We show that the testing statistics follow chi-square distribution in theory. The numerical simulations and a real data analysis verify our proposed methods are valid for testing the long memory parameter in stationary ARFIMA models.
  • Statistical Inference of Mode Regression with Adaptive Lasso#br#
    YE Wuyi, XU Yincong, JIAO Shoukun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 107-121. https://doi.org/10.3969/j.issn.1001-4268.2024.01.007
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    In this paper, an adaptive Lasso mode regression model is proposed to solve the problem of variable selection in mode regression model. Compared with the traditional mean regression and median regression, mode regression is robust when the distribution is heavy-tail or asymmetric. Kernel estimation is widely used in mode regression. When coping with high dimension, the method will result in calculation errors that hard to ignore. In this paper, the adaptive Lasso penalty is added to estimated parameters based on the mode regression model of the kernel estimation method, and the independent variables with low contribution rate are effectively eliminated. Therefore, the method can improve the accuracy of the calculation. The calculation method is described in detail in this paper, and this paper proposes the estimation methods of the parameters of the model and the asymptotic normality of the estimated values under some regular conditions. The simulation experiment and empirical analysis are performed to investigate the properties of the proposed method in finite sample. Compared with the traditional mode regression model and the mean regression model, the mode regression model with adaptive Lasso penalty greatly improves the accuracy of parameter estimation.
  • Worst-Case Distortion Risk Measure with Application to Robust Portfolio Selection#br#
    YAN Xuechen, LI Lu, WANG Yashi
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 122-138. https://doi.org/10.3969/j.issn.1001-4268.2024.01.008
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Portfolio selection depends heavily on the underlying distribution of loss. When the distribution information of loss can only be observed through a limited sample of data, robustness of the portfolio selection model is of crucial importance. Assuming that the
    underlying distribution of loss has a known mean and variance and lies within a ball centred on the reference distribution with the Wasserstein distance as the radius, this paper proposes a robust portfolio strategy model based on the distortion risk measure and translates it into a simpler equivalent form. Furthermore, simulation and empirical study are used to demonstrate the validity of the model.
  • Some Properties of Fractional Kinetic Equation with Gaussian Noise Rough in Space#br#
    LU Weidong, LIU Junfeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 139-156. https://doi.org/10.3969/j.issn.1001-4268.2024.01.009
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    In this article, we study a class of fractional kinetic equation driven by Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst index H<1/2 in space. By using the techniques of Malliavin calculus, we prove the existence of the solution in the Skorohod sense and establish the upper and lower bounds for the moments of the solution. We also deduce the H\"{o}lder continuity of the solution with respect to the time and space variables.
  • Overview of Robust Variable Selection Methods for High-Dimensional Linear Regression Model#br#
    ZOU Hang, JIANG Yunlu
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2024, 40(1): 157-181. https://doi.org/10.3969/j.issn.1001-4268.2024.01.010
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    With the advance of the era of big data, high-dimensional data are frequently collected in many research fields such as economics, finance, and biomedicine. One of the characteristics of high-dimensional data is that the variable dimension p increases with the increase of the sample size n and usually exceeds the sample size. At the same time, outliers are also prone to appear in high-dimensional data. Therefore, how to overcome the influence of outliers on high-dimensional statistical inference, so as to obtain a
    more accurate model, is one of the hot issues in current statistical research. This paper is an overview of robust variable selection methods under high-dimensional linear models. Specifically, first of all, we introduce three indicators to evaluate robustness: influence function, breakdown point and maximum deviation. Secondly, it focuses on the selection methods of robust variables, including response variables with outliers, response variables and covariates with outliers, high breakdown point and efficient variable selection methods. Then, the related algorithms are introduced, and different variable selection methods are compared through simulation and examples. Finally, the problems of high-dimensional robust effective variable selection methods and the possible development direction in the future are briefly discussed.
Chinese Journal of Applied Probability and Statistics (Bimonthly)
（started publication in 1985）
Superintendent: Chinese Society of Probability and Statistics
Editor-in-Chief: Chen Mufa
ISSN 1001-4268
CN 31-1256
Mailing code: 4-414
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