20 February 2007, Volume 23 Issue 1

    

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学术论文
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  Some Measures of the Severity of Ruin and the Cost of Recovery in the Classical Risk Model Disturbed by Diffusion

  Zhang Chunsheng, Chen Xuemin

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 1-10.

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  In this paper we consider the maximal severity of ruin and the cost of recovery
  which are proposed by Picard (1994). We will improve and extend the results in
  Picard (1994) from the classical risk model to the model disturbed by diffusion.
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  The Central Limit Theorem for Markov Chains in Markovian Environments

  Guo Mingle

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 11-17.

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  In this paper, a central limit theorem for function of countable Markov chains in
  Markovian environments is investigated. Moreover, some sufficient conditions on
  the jointly Markov chains and sample function of the jointly Markov chains are given.
  At last, $R_{\theta}$-chains are systematically studied, some sufficient contions
  for the central limit theorem to hold for function of Markov chains in Markovian
  environments are obtained.
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  A Test for Rigid Structure of the Grouped Points in High-Dimensional Data

  Zhu Lixin, Wang Huiwen, Liu Qiang

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 18-24.

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  In this paper, we propose a test to check whether in motion, the point groups of
  high-dimensional longitudinal data keep a rigid structure and suggest a definition
  of transmutation coefficient of the groups. In terms of testing the rigid structure,
  the major characters of the motion of the groups can be handled so that the prediction for the motion in future can be expected. To demonstrate the rationale and potential use of the method, simulations and an analysis for the diversity of economic changes between the city group in the east China and the city group in the west China have been carried out.
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  The Variable Selection in Covariance Adjusted Estimates

  Yin Suju, Wang Songgui

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 25-30.

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  In this paper we study the problem about how to select the covariables. A new test approach by using the canonical correlation is proposed, the approximate distribution of the test statistics is gived. A simulation comparision is made under three forms of covariance matrices which are adopted very often in the economy, biology and medicine. Our results show that the necessity of covariable selection and the good properity of the canonical correlation test method.
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  Efficient Portfolio and No-Arbitrage Analysis in General M-V Model

  Jiang Chunfu, Dai Yonglong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 31-41.

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  In this paper, we investigate efficient portfolio in general M-V model with singular
  covariance matrix. This paper not only establishes the necessary and sufficient condition for existing efficient portfolio in the stock market, but derives the general solutions of efficient portfolio and some properties of efficent frontier. Finally we make no-arbitrage analysis for the stock market with singular covariance matrix, obtain the necessary and sufficient condition for not existing abritarge portfolio, which proves the conjecture proposed by Szeg\"{o}.
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  Coverage Accuracy of Confidence Intervals for a Conditional Probability Density Function

  Lei Qingzhu, Qing Yongsong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 42-50.

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  Point-wise confidence intervals for a conditional probability density function are
  considered. The confidence intervals are based on the empirical likelihood. Their
  coverage accuracy is assessed by developing Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable.
  
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  Bayes Statistical Inference on General $\xd$-Shock Model with Zero-Failure Data

  Li Zhehui, Liu Zhi, Niu Yi

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 51-58.

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  In this paper, we use Bayesian method to study the estimation problem of the parameters $\xd_1$ and $\xd_2$ of the $\xd$-shock model associated with a Poisson process with intensity $\xl$ under zero-failure data, where the system fails when the length of an interval between two success shocks does not fall in a prespecified interval $[\xd_1, \xd_2]$. By choosing $U(0,1)$ and a Beta distribution as the prior distribution of the parameters respectively, we obtain the Bayesian and hierarchical Bayesian estimators of threshold level $\xd_1$ and $\xd_2$.
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  The Robustness of Bayes Linear Unbiased Estimations under Misspecified Prior Assumption

  Zhang Weiping, Wei Laisheng

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 59-67.

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  The Bayes linear unbiased estimator (BLUE) of parameters is derived for general linear model under misspecified prior assumption. The robustness of BLUE over ordinary least square estimator (LSE) are shown in terms of mean square error matrix criterion and Pitman closeness criterion, the bounds of the relative efficiency of estimators are obtained.
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  Likelihood Ratio Test and Power Analysis of Repeated Measures Models

  He Zhiyan, Liao Jingyu

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 68-76.

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  For the repeated measures experimental model with compound symmetry sample covariance matrix, asymptotic null distributions and non-null distributions of likelihood ratio test statistic are given, and the power are analyzed.
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  The Two-Step Sequential Mesh Test for A Proportion

  Pu Xiaolong, et.al

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 77-83.

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  The sequential probability ratio test (SPRT) is widely used, while the
  sequential mesh test is much powerful. In this article we propose the
  two-step sequential mesh test. The results show that it is better than
  the sequential mesh test.
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  Optimal Utility with Side Information and its Affect

  Xiong Dewen

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 84-90.

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  We first consider the problem of representation of the $Q$-martingale $\{\wt{\Lambda}_t :=\ep^Q[\Lambda_T|{\cal G}_t]\}$. Then we consider a market of a stock price affected by a stochastic factor, in which there exists a insider who only knows the price information and a side information. We consider his problem of optimal utility for terminal wealth with and without side-information, and obtain a form of optimal terminal wealth in two cases. Finally, we compare these two cases for the logarithmic utility, and analyze the influence of the `side information'.
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  The Statistical Analysis of Orthogonal Saturated Design

  Zhang Xiaoqing

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(1): 91-101.

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  The paper uses the non-central $F$ statistic to research the multi-levels orthogonal saturated design, and has produced a kind of estimate about the variance and the non-central parameter. Some satisfying results are obtained when it is applied in the orthogonal saturated design.