20 November 2006, Volume 22 Issue 4

    

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学术论文
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  Nonparametric Variance Function Estimate in Generalized Linear Models

  CHEN Xia

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 337-346.

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  This article advances an improved estimate $\wh\sigma_{n}(u)$ of $\sigma(u)$, and under some conditions, proves $\sup\limits_{u}|\wh\sigma_{n}(u)-\sigma(u)|\rightarrow0$in probability with faster speed.
论文
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  A Strong Invariance Principle for Associated Sequences of Gaussian Random Variables

  WANG Wensheng

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 347-357.

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  In this paper, by applying the Skorohod martingale embedding theorem, we prove a strong invariance principle for an associated sequence of Gaussian random variables under the restrictions that the sequence is Gaussian and the covariance coefficients of the sequence decay with power decay rates. As consequences, the law of the iterated logarithm and Chung's law of the iterated logarithm for associated sequences of Gaussian random variables are obtained.
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  A Note on the Self-Normalized Large Deviation

  SHAO Qiman

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 358-362.

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  Let $X_1,X_2,\cdots$ be a sequence of i.i.d. random variables. Shao (1997) established a self-normalized large deviation without any moment assumption. However, the proof of the upper bound was quite complicated. In this note we give a much simpler proof.
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  Case-Deletion Measure Based on $Q$-Function for Exponential Family Nonlinear Mixed Models

  FEN Yu

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 365-371.

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  Based on $Q$-function introduced by Zhu \& Lee (2001), this paper proposes some case-deletion measures for assessing the influence of an observation in exponential family nonlinear mixed models. The key idea is to treat the random effects as hypothetical missing data and works with the conditional expectation of the complete-data log-likelihood in the EM algorithm. An example illustrates our method.
  
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  Ruin Analysis for Erlang(2) Risk Process and American Put Option

  DING Zhaopeng

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 372-386.

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  In the classical risk theory, the risk of the accumulative claims follows Poission
  process. We will consider Erlang(2) risk process with the time between two claims
  following Erlang(2) distribution which always appears in control theory. In this paper,we consider an auxiliary function $\phi(\cdot)$ which involves the time of ruin, the surplus immediately before ruin, and the deficit at the time of ruin for our model within the three variables are essential and principal for the study of risk process.This auxiliary function has been studied by Willmot and Lin (1999) in the classical continuous time risk model. Motivated by the exposition in Gerber and Shiu (1997)and Willmot and Lin (2000), the first important result is to find the joint distributiondensity function of $U(T-)$ and $|U(T)|$ which is convenient to get the expression of $\phi(\cdot)$. But our approach is rather different from the technique for the classical risk model because of the distinct internal characteristic between two models. Influenced by the ideas in Gerber and Landry (1998) and Gerber and Shiu (1999), we will determine the optimal exercise price for an American put option whose foundation property price follows some risk process as an application.
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  Assessing Local Influences in a Multivariate $t$-Model with Uniform Structure

  ZHANG Huaixiong, ZOU Qingming

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 387-400.

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  The present paper is devoted to the problem of assessing local influences in
  a multivariate $t$-model with uniform structure. The effects of some minor
  perturbation on the statistical inference are considered based on Cook's
  curvature measure. This leads to the largest curvature direction which is the
  statistic mainly concerned in the local influence analysis. As an application,
  a common covariance-weighted perturbation is thoroughly discussed.
  
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  Empirical Likelihood Method under Stratified Random Sampling Using Auxiliary Information and the Information in the Strata Population Size

  WU Changchun, ZHANG Runchu

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 401-409.

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  The empirical likelihood method under stratified random sampling is used for getting estimators of finite population parameters, we show in this paper that the empirical likelihood approach is well-suited to incorporate auxiliary information and can accommodate this information contained in the population size for each stratum quite naturally. Our results show that it can lead to efficient estimators.
  
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  The Moments of the Time of Ruin, the Surplus before Ruin, and the Deficit at Ruin in the Risk Models with Constant Interest Rate

  LIU Li, ZHU Liping

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 410-418.

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  In this paper, by using the form of the solution for the expected value of a discounted function in the risk models with constant interest rate, properties of the joint and marginal moments of the time of ruin, the surplus before ruin and the deficit at ruin are studied, and recursive equations are obtained respectively.
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  The Estimation of The $r$th Original Mement of Interval Censored Data

  DENG Wenli, ZHENG Zukang

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 419-428.

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  In reliability and survival analysis, the data obtained in modelling failure
  times are often interval censored. When interval censoring arises, almost all
  traditional statistical methods cannot work any more.In this paper unbiased transformation method will be used to estimate the $r$th original mement of interval censored data. When the distribution of the censoring variables is specified, a class of estimators having strong consistency (with the rate of $O(n^{-1/2}(\log\log n)^{1/2})$) and asymptotic normality have been got.

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  On Robustness of LSE in Terms of Error Distributions

  LIU Xiangrong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 429-437.

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  In this paper, we explore the varing range of the error distributions within which
  the LSE is the best linear estimator in the sense of minimizing the MSE matrix. We also give the maximal class of distributions of error term for which the LSE possesses a certain kind of robustness.