20 February 2009, Volume 25 Issue 2

    

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学术论文
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  A Law of the Iterated Logarithm for MLE Based on Random Censoring Model with Incomplete Information

  Song Yijun,Li Buxi,Li Jihong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 113-125.

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  In this paper, we prove that MLE for life distributed parameter converges to the true parameter at the rate of the law of iterated logarithm. At the same time, we verify that Weibull distribution and lognormal distribution are stratified with
  conditions $(\Phi)$ proposed here.
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  Finite and Infinite Dimensional Stochastic Differential Equations with Non-Lipschitzian Coefficients

  Wang Fengyu,Wang Jieming

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 126-134.

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  A recent result of Fang and Zhang concerning the pathwise uniqueness of solutions to non-Lipschitzian stochastic differential equations is refined. As an application, a class of infinite-dimensional stochastic differential equations over lattice fields are proved to have unique solutions.
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  On Weighted Total Least Absolute Deviations

  Yang Guiyuan, Yang Guiyuan

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 135-142.

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  The paper demonstrates the existence of the optimal straight line under the minimum of weighted total least absolute deviation, and suggests the two necessary conditions that the optimal straight line should satisfy, and provides evidence for the calculation of accurate and optimal solution.
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  Estimation of Structural Reliability for a Nested Multivariate Exponential Distributed Stress

  Wang Hui,Ye Cinan,Yan Guangle

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 143-154.

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  We study a kind of stress-strength structural reliability model with stress being nested multivariate exponential distributed and strength being one-dimensional exponential distributed in this paper. On condition that strength parameter
  unknown and stress parameters known as well as contrary situations, the estimators $\wh{P}_{A1}$ and $\wh{P}_{A2}$ of the structural reliability $P_{A}$ are proposed and their consistency and asymptotic normality are discussed, meanwhile, the estimators' confidence intervals are also shown. Finally, we randomly simulate the estimators $\wh{P}_{A1}$ and $\wh{P}_{A2}$ of $P_{A}$ with the satisfactory results.
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  Spectral Decomposition Method for the Covariance Matrix of Variance Components Model

  Liu Wei,Wang Songgui,Dong Ping

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 155-163.

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  For the balanced variance components model, the main contribution of this thesis is to provide a new spectral decomposition method for the covariance matrix. The computation of this new method is simple, it can give the number of different eigenvalues of covariance matrix and closed form of the projective matrices corresponding to its eigenvalues. Based on this new method we discuss several properties of variance components model. Further more, this thesis studies general variance components model. Firstly, we give the definition of simple spectral decomposition and obtain a necessary and sufficient condition of existence of simple spectral decomposition, then discuss some characters. To this kind of models, the application in statistical inference of simple spectral decomposition is also discussed.
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  A Comparativen Study on Confidence Interval of $C_p$ in Terms of Standard Deviation Estimated

  Kong Xiangfen,He Zhen,Che Jianguo,Jin Huibin

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 164-170.

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  The estimator of population standard deviationcan be represented by sample standard deviation $s$, $s/c_4$, \ol{R}/d_2$ and $\wh{\sigma}_{\text{TOTAL}}$ based on MVA, espectively. This paper presents the estimation of $C_p$ and C_{pk}$ as well as the confidence interval of $C_p$ using different
  estimation methods of population standard deviation. Further, each
  estimation method is analyzed in an example.
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  Asymptotic Properties of Estimation in GeneralizedPartial Linear Mixed Models

  Zhang Hao, Zhu Zhongyi

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 171-184.

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  Semiparametric models are useful in sychological, biological and medical application. Zhang (1998) used
  maximum penalized likelihood estimation (MPLE) to estimate both of
  the parametric and nonparametric parameters. Unfortunately, MPLE
  proposed by Zhang (1998) can only be applied to the Gaussian Models.
  In general, in order to estimate the parametric and nonparametric
  part in generalized partial linear mixed models, we choose to treat
  the random effects as the missing data and construct a Monte Carlo
  version of the EM algorithm. Based on the MCNR algorithm proposed by
  McCulloch (1997), we, in this paper, extend the algorithm to the
  eneralized partial linear mixed models (GPLMM) so that it may
  estimate both of the parameters and nonparameters simultaneously. In
  the new algorithm, we approximate the nonparametric function in
  GPLMM by P-spline and use GCV to choose the smoothing parameter.
  Meanwhile, we also give the proofs and the asymptotic properties of
  the estimators. Finally, in order to test the reliability of the
  method, the proposed algorithm is illustrated in the simulation
  analysis and one real data set.
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  Evaluating the Randomness Based on Spectral Density

  Zhu Liping,Lin Longnian

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 185-191.

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  To evaluate the randomness of a sequence, we propose a graphic approach based on spectral density. When the scatter points in the graph exhibit a linear structure, we conclude that the sequence is random. To illustrate the basic idea
  of this method, one synthetic example is carried out to assess the randomness of pseudo-random sequence generator. This method is also applied to a real data to investigate the serial correlation among a sequence. Both examples have evidenced the efficacy of our proposed graphic approach.
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  Strong Stability of Linear Forms with Pairwise\\NQD Random Sequences

  Wan Chenggao,Chen Fen

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 192-200.

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  In this paper, we discuss strong stability of linear forms in pairwise NQD random sequences and get sufficient conditions for strong stability of linear forms with different distributions pairwise NQD random sequences.
综合报告
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  Histogram Theories and Optimal Histogram Construction Algorithms

  Zhang Jianfang,Wang Xiuxiang

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 201-214.

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  Histogram is the most widely used density estimator and data analysis tool. It is completely determined by two parameters: the bin width and one of the bin edges. However, many professional statisticians have no really definitive answers and simply give some intuitive advises when face to choose these two parameters. Even most statistical packages use the rules of thumbs for selecting the number of bins as a default. In this paper, we will present the histogram theories and optimal histogram construction algorithms that have been recently proposed. The methods of how to construct the data-based histograms are the
  emphasis of this paper.