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 2009 Vol.25 Issue.2,Published 2009-02-20
 学术论文
 113 A Law of the Iterated Logarithm for MLE Based on Random Censoring Model with Incomplete Information Song Yijun,Li Buxi,Li Jihong 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 withconditions $(\Phi)$ proposed here. 2009 Vol. 25 (2): 113-125 [Abstract] ( 1951 ) [HTML 0KB] [ PDF 245KB] ( 1416 )
 126 Finite and Infinite Dimensional Stochastic Differential Equations with Non-Lipschitzian Coefficients Wang Fengyu,Wang Jieming 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. 2009 Vol. 25 (2): 126-134 [Abstract] ( 1890 ) [HTML 0KB] [ PDF 207KB] ( 1495 )
 135 On Weighted Total Least Absolute Deviations Yang Guiyuan, Yang Guiyuan 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. 2009 Vol. 25 (2): 135-142 [Abstract] ( 1990 ) [HTML 0KB] [ PDF 218KB] ( 1526 )
 143 Estimation of Structural Reliability for a Nested Multivariate Exponential Distributed Stress Wang Hui,Ye Cinan,Yan Guangle 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 parameterunknown 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. 2009 Vol. 25 (2): 143-154 [Abstract] ( 1964 ) [HTML 0KB] [ PDF 236KB] ( 1181 )
 155 Spectral Decomposition Method for the Covariance Matrix of Variance Components Model Liu Wei,Wang Songgui,Dong Ping 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. 2009 Vol. 25 (2): 155-163 [Abstract] ( 1964 ) [HTML 0KB] [ PDF 229KB] ( 1443 )
 164 A Comparativen Study on Confidence Interval of $C_p$ in Terms of Standard Deviation Estimated Kong Xiangfen,He Zhen,Che Jianguo,Jin Huibin 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 differentestimation methods of population standard deviation. Further, eachestimation method is analyzed in an example. 2009 Vol. 25 (2): 164-170 [Abstract] ( 2303 ) [HTML 0KB] [ PDF 229KB] ( 1733 )
 171 Asymptotic Properties of Estimation in GeneralizedPartial Linear Mixed Models Zhang Hao, Zhu Zhongyi Semiparametric models are useful in sychological, biological and medical application. Zhang (1998) usedmaximum penalized likelihood estimation (MPLE) to estimate both ofthe parametric and nonparametric parameters. Unfortunately, MPLEproposed by Zhang (1998) can only be applied to the Gaussian Models.In general, in order to estimate the parametric and nonparametricpart in generalized partial linear mixed models, we choose to treatthe random effects as the missing data and construct a Monte Carloversion of the EM algorithm. Based on the MCNR algorithm proposed byMcCulloch (1997), we, in this paper, extend the algorithm to the eneralized partial linear mixed models (GPLMM) so that it mayestimate both of the parameters and nonparameters simultaneously. Inthe new algorithm, we approximate the nonparametric function inGPLMM by P-spline and use GCV to choose the smoothing parameter.Meanwhile, we also give the proofs and the asymptotic properties ofthe estimators. Finally, in order to test the reliability of themethod, the proposed algorithm is illustrated in the simulationanalysis and one real data set. 2009 Vol. 25 (2): 171-184 [Abstract] ( 2582 ) [HTML 0KB] [ PDF 284KB] ( 1802 )
 185 Evaluating the Randomness Based on Spectral Density Zhu Liping,Lin Longnian 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 ideaof 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. 2009 Vol. 25 (2): 185-191 [Abstract] ( 2021 ) [HTML 0KB] [ PDF 5612KB] ( 1410 )
 192 Strong Stability of Linear Forms with Pairwise\\NQD Random Sequences Wan Chenggao,Chen Fen 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. 2009 Vol. 25 (2): 192-200 [Abstract] ( 1655 ) [HTML 0KB] [ PDF 208KB] ( 1259 )
 综合报告
 201 Histogram Theories and Optimal Histogram Construction Algorithms Zhang Jianfang,Wang Xiuxiang 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 theemphasis of this paper. 2009 Vol. 25 (2): 201-214 [Abstract] ( 2749 ) [HTML 0KB] [ PDF 1049KB] ( 3790 )
 应用简报
 215 2009 Vol. 25 (2): 215-218 [Abstract] ( 1609 ) [HTML 0KB] [ PDF 144KB] ( 1364 )
 219 2009 Vol. 25 (2): 219-223 [Abstract] ( 1409 ) [HTML 0KB] [ PDF 149KB] ( 1201 )
 学术活动报道
 224 2009 Vol. 25 (2): 224-224 [Abstract] ( 1414 ) [HTML 0KB] [ PDF 48KB] ( 1297 )

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