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2018 Vol.34 Issue.5,Published 2018-10-26

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441 Stochastic Differential Game for DC Pension under Stochastic Interest Rate
YANG Peng

This paper investigate a stochastic differential games for DC (defined contribution plans) pension under Vasicek stochastic interest rate. The finance market as the hypothetical counterpart, the investor as pension the leader of game. Our goal is through the game between pension plan investor and financial market, obtain optimal strategies to maximizes the expected utility of the terminal wealth. Under power utility function, by using stochastic control theory, we obtain closed-form solutions for the value function as well as the strategies. Finally, explain the research results in the economic sense, and though numerical calculation given the influence of some parameters on the optimal strategies

2018 Vol. 34 (5): 441-449 [Abstract] ( 130 ) [HTML 1KB] [ PDF 673KB] ( 332 )
450 Asymptotic Properties of Nonparametric Intensity Estimation for Replicated Spatial Point Patterns
ZHAO Jin; ZHOU Xiuqing

A kernel-type nonparametric estimator of the intensity function for inhomogeneous spatial point patterns with replicated data is proposed. Asymptotic expansion of the mean square error is derived and the rate of convergence of the integrated square error is also investigated. Two methods, least-square and composite likelihood cross-validation, for selecting the bandwidth are described. The performance of the two procedures are illustrated using simulation data.

2018 Vol. 34 (5): 450-462 [Abstract] ( 107 ) [HTML 1KB] [ PDF 634KB] ( 265 )
463 Two Notes on Energy Distance
CHEN Minqiong

The definition of Brownian distance is presented and it's proved that Brownian distance coincides with the energy distance with respect to Brownian motion. Energy distance for dependent random vectors is also given and the asymptotic distribution is derived under null hypothesis. A simple numerical simulation result shows that the method for paired-sample test based on energy distance can distinguish the distributions of the paired variables more effectively than the
classical t-test and Wilcoxon signed rank test.

2018 Vol. 34 (5): 463-474 [Abstract] ( 125 ) [HTML 1KB] [ PDF 425KB] ( 310 )
475 Confidence Intervals for the Common Mean of Several Log-normal Populations Using Confidence Distributions
NIU Cuizhen; GUO Xu; LI Qiuyue

The log-normal distribution is a common choice for modeling positively skewed data arising from many practical applications.This article introduces a new method of constructing confidence interval for a common mean shared by several log-normal populations through confidence distributions, which combines all information from independent sources. We develop a non-trivial weighting approach by taking account of the sample variances of related quantities to enhance efficiency. Combined confidence distributions are used to construct confidence intervals for the common mean and a simplified version of one existing method is also proposed. We conduct simulation studies to evaluate the performance of the proposed methods in comparison with existing methods. Our simulation results show that the weighting approach yields shorter interval length than the non-weighting approach. The newly proposed confidence intervals perform very well in terms of empirical coverage probability and average interval length. Finally, applications of the proposed methodology is illustrated through three real data examples.

2018 Vol. 34 (5): 475-491 [Abstract] ( 122 ) [HTML 1KB] [ PDF 646KB] ( 339 )
492 The Statistical Analysis of Parameter Model with an Assumed Copula for Dependent Censoring Data
DENG Wenli; WU Zixing; CAI Ming

In collecting clinical data, data would be censored due to competing risks or patient withdrawal. The statistical inference for censoring data is always based on the assumption that the failure time and censoring time is independent. But in practice the failure time and censoring time are often dependent. Dependent censoring make the job to deal with censoring data more complicated. In this paper, we assume that the joint distribution of the failure time variable and
censoring time variable is a function of their marginal distributions. This function is called a copula. Under prespecified copulas, the maximum likelihood estimators for cox proportional hazards models are worked out. Statistical analysis results are carried by simulations. When dependent censoring happens, the proposed method will do better than the traditional method used in independent situations. Simulation results show that the proposed method can get efficient estimations.

2018 Vol. 34 (5): 492-500 [Abstract] ( 107 ) [HTML 1KB] [ PDF 513KB] ( 305 )
501 Vector Parameter for Ridge Regression
ZHU Shangwei; LI Jinghua

In this paper, a vector parameter method for ridge regression is proposed. We choose the negative gradient of mean square error as vector direction and decide vector norm with the expectation constrains both of mean square error and of residual error. We come to conclusions that the mean square error is a decreasing function of vector norm while the residual error a increasing one. It is the monotonicity of the errors that leads to our expectation constrains. Since two conflict constrains are under consideration, our vector parameter ridge regression is expected to bear both satisfactory mean square error and acceptable residual error. Finally, a multi-collinearity model is given as an example.

2018 Vol. 34 (5): 501-514 [Abstract] ( 123 ) [HTML 1KB] [ PDF 697KB] ( 301 )
515 M-estimation and Quantile Estimation in the Presence of Auxiliary Information under Strong Mixing Sample
LI Yinghua; LI Yuan; QIN Yongsong

In this paper, we apply the empirical likelihood technique to propose a new class of M-estimators and quantile estimators in the presence of some auxiliary information under strong mixing samples. It is shown that the proposed M-estimators and quantile estimators are consistent and asymptotically normally distributed with smaller asymptotic variances than those of the usual M-estimators and quantile estimators.

2018 Vol. 34 (5): 515-532 [Abstract] ( 98 ) [HTML 1KB] [ PDF 482KB] ( 288 )
article
533 Reconstructing the Sanxian's Music Score by a Birth--Death Matrix
CHEN Mu-Fa

The Sanxian is a traditional Chinese three-stringed plucked instrument. Its music can be generated by tridiagonal complex matrices. The sound people hear is determined by its spectrum and naturally requires that the matrix has a real spectrum. As in quantum mechanics, the description of the model is a complex operator and the observable measurement is real. In other words, the tridiagonal complex matrix described is a self-adjoint operator on the complex inner product space with respect to a measure. It is well known that the birth--death Q matrix can be matched and naturally self-adjointed. We will introduce the latest
representative results: for a fairly wide range of self-adjoint tridiagonal complex matrices, a birth--death Q matrix can always be constructed to make both isospectral (in simple words, both have the same eigenvalues). This problem is simple and easy to understand. But we have studied it from three different perspectives: probability theory, statistical physics and computational mathematics at different times, and have gone through a long time of exploration.

2018 Vol. 34 (5): 533-545 [Abstract] ( 142 ) [HTML 1KB] [ PDF 2573KB] ( 301 )
546
2018 Vol. 34 (5): 546-550 [Abstract] ( 74 ) [HTML 1KB] [ PDF 0KB] ( 161 )
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