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Current Issue
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 with
conditions $(\Phi)$ proposed here.
2009 Vol. 25 (2): 113-125 [
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1951
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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 [
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1890
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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 [
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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 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.
2009 Vol. 25 (2): 143-154 [
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1964
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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 [
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1964
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1443
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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 different
estimation methods of population standard deviation. Further, each
estimation method is analyzed in an example.
2009 Vol. 25 (2): 164-170 [
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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) 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.
2009 Vol. 25 (2): 171-184 [
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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 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.
2009 Vol. 25 (2): 185-191 [
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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 [
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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 the
emphasis of this paper.
2009 Vol. 25 (2): 201-214 [
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应用简报
215
2009 Vol. 25 (2): 215-218 [
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144KB] (
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219
2009 Vol. 25 (2): 219-223 [
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学术活动报道
224
2009 Vol. 25 (2): 224-224 [
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