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• 学术论文
Luo Ji
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(3): 312-318.
EM algorithm is one of the data augmentation algorithms, which usually are used to obtain estimate of the posterior mode of observed data recent years. However, because of its difficulty in calculating the explicit expression of the integral in E step, the application of EM algorithm is limited. While Monte Carlo EM algorithm solves the problem well. Owing to effectively facilitating the integral in E step of EM algorithm by Monte Carlo simulating, Monte Carlo EM algorithm has been successfully used to a wide range of applications. There is, however, the same shortage for EM algorithm and Monte Carlo EM algorithm, that the convergence rate of the two algorithms is linear. So this paper proposes the acceleration of Monte Carlo EM Algorithm, which is based on Monte Carlo EM Algorithm and Newton-Raphson algorithm, to improve the convergence rate. Thus the acceleration of Monte Carlo EM Algorithm has the advantages of both Monte Carlo EM Algorithm and Newton-Raphson algorithm, that is to say it facilitates E step by Monte Carlo simulation and also has quadratic convergence rate in a neighborhood of the posterior mode. Later its excellence in convergence rate is illustrated by a classical example.
• 学术论文
Lu Zhifeng,Wang Juan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 354-364.
This paper extends the (generalized)
Beta distribution to the (generalized) multivariate Beta
distribution. We also study the moment generating function of
multivariate Beta distribution, obtain the marginal distribution,
conditional distribution and regression function of the generalized
multivariate Beta distribution.
• 学术论文
Ji Yunqi, Zhu Zhongyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(5): 541-553.
Marginal regression model and its associated generalized estimating equation (GEE) are becoming increasingly being used in longitudinal studies. Pepe and Anderson (1994) pointed out that there is an important assumption called PA condition behind GEE method. If the assumption is violated and nondiagonal working correlation matrix is used in GEE, the statistical inference may be
deficient. This paper focused on PA condition's influence on the testing of regression coefficients in GEE method by theoretic and numeric analysis. Due to the violation of the PA condition, the distributions of Wald statistics and Score statistics based on GLS estimators are noncentral $\chi^{2}$ distributions. The efficiency of testing based on the GEE method is largely influenced.
• 学术论文
Wu Liucang,Li Huiqiong,Wu Xiaokun, Jiang Shaoping
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(3): 254-264.
Consider the variance component model $\ep Y=X\beta,\;\cov(Y)=\tsm_{i=1}^m\theta_iV_i$, where $X$: $n\times p$ and $V_i\geq0\;(i=1,2,\cdots,m)$ are known, $\beta\in R^p$, $\theta_i\geq0$ or $\theta_i>0$ $(i=1,2,\cdots,m)$ are parameters. In this paper, when $\mu(X)\subset\mu(V)$, the sufficient and necessary conditions for a linear estimable estimator of $S\beta$ to be admissible in the class of all linear estimators are given under quadratic loss function.
• 学术论文
Yu Peng, Tong Xinwei, Feng Jufu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(5): 475-483.
In this paper we propose an unsupervised classification algorithm which is based on Gaussian mixture models. Thinking that EM algorithm will result in a local optimal resolution of Gaussian mixture models in parameter estimations, we substitute invert Wishart distribution for Jeffery prior. Experiments show that this
algorithm improves correct rates and decreases time while estimating
classifications.
• 论文
CUI Hengjian
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 321-328.
This paper defines $t$-type regression estimator for the linear functional
errors-in-variables (EV) models, the EM algorithm for $t$-type estimators in
the ordinary linear model and linear functional EV model is given. Moreover,
the consistency of $t$-type estimators for linear EV model is also obtained.
Simulations are shown that performance of the t-type estimators by EM algorithm
is quite well.
• 论文
WANG Wensheng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 347-357.
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.
• 学术论文
Meng Xianhua, Wang Jinglong,Wu Xianyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(1): 95-101.
In this paper, we give an analytical comparison between Bonferroni and Scheff\'{e} simultaneous confidence intervals for themean of a multivariate normal distribution, which concludes that the Bonferroni intervals are shorter than the Scheff\'{e} intervals when the dimension of the mean vector is between 2 and 12.
• 学术论文
Zheng Linrui, Zhu Zhongyi, Lu Yiqiang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(3): 329-336.
The assumption of homoscedasticity is commonly concerned in regression analysis. According to the Laplace spread theory, we study the variance component testing in discrete semiparametric generalized linear model with random effects for longitudinal data, and the score statistic is obtained. An example and some simulation studies are implenented to verify the efficiency of our method.
• 论文
ZHU Liping, LU Yiqiang; MAO Shisong
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(2): 137-150.
Mixed exponentially distribution failure time distributions play an important role in life time data analysis. But we may encounter enormous difficulties when we try to estimate the model by traditional methods such as maximize likelihood (ML) estimation and moment estimation. In this paper, we employ the EM algorithm to obtain the ML estimation for the mixed exponential model under the normal stress life time test with full data or censored samples. The iteration formula are given in the paper. Simulations are also made to evidence the performance of estimation.
• 论文
HE Shuyuan, AI Mingyao, SUN Xinli
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 237-244.
Let $\{X_t\}$ be a stationary signal process interfered by an white noise $\{Y_t\}$. The signal $X_t$ is detected and observed only when $X_t>Y_t$, otherwise only the white noise $Y_t$ is observed. This model is called the left censored model and the observation is called the left censored observation. In this paper we use the nonparametric MLE of the marginal distributions of $X_t$ and $Y_t$ to construct estimates of the mean, autocovariance and autocorrelation functions of the original signal process $\{X_t\}$. The strong consistency of the estimates is derived. When $\{X_t\}$ is a causal autoregression process, consistent estimates of the autoregression parameters are provided.
• 学术论文

TIAN Ping, XUE Liugen

CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 369-376.
In this paper, we consider the following semiparametric regression model for
longitudinal data: $y_{ij}=x_{ij}'\beta+g(t_{ij})+e_{ij}$. The estimators of $\beta$ and $g(\cdot)$ are obtained by using the least squares and usual nonparametric weight function method, the asymptotic normality of the estimator of $\beta$ and the optimal convergence rate of the estimator of $g(\cdot)$ are proved under the suitable conditions. Some simulations are conducted to demonstrate the finite sample performances of the estimation procedures.
• 论文
WEI Bocheng, XIE Fengchang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 252-262.
Based on the EM algorithm and Laplace approximation, this paper presents a method of influence analysis for zero inflated longitudinal count data models. To detect the influential observations in clustered count data with excess zeros, we regard the random effects as the missing data and put certain weight to the data with zero values in ZI longitudinal data models. According to this fact, we develop the influence method for the model based on the conditional expectation of the
complete-data log-likelihood function and the associated $Q$-distance function
under the EM algorithm. The Laplace approximation is also employed for integral
computing in E-step. Then the case-deletion model and the local influence analysis are investigated for the model and several diagnostic measures are obtained. Finally, a numerical example of the real count data is given to illustrate the results in this paper.
• 学术论文
Xie Fengchang,Wei Bocheng,Lin Jinguan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(6): 659-671.
ZI (zero-inflated) data are data with overmuch zeroes.
The ZI data have been commonly encountered in a wide variation of
disciplines, and have been a hot topic since last decade. In this
paper, we first present the actual significance of ZI data via two
examples. Then we demonstrate the general situation and latest
improvement of statistical analysis for zero-inflated data.
Additionally, zero-inflated models, zero-inflated mixed models, and
the estimation methods and some diagnostic problems are surveyed
systematically. The relevant work done by authors in recent years
are also introduced. Finally, several potential topics to be studied
are listed.
• 学术论文
Tian Maozai, Wu Xizhi, Li Yuan, Zhou Pengpeng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(3): 327-336.
Many of the previous studies have emphasized the effects of students' economic background and psychological factors on their achievements. Less attention has been paid, however, to the external pressure factors, such as parent's push and peer's push on achievements. This article attempts to address the interesting and important research topic and to give an in-depth longitudinal study of American youth using a so called double-kernel'' nonparametric quantile regression approach. Several interesting findings are useful for parents, especially for
educational policy makers and consultants.
• 论文
CHAI Genxiang, SUN Yan
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 245-251.
In this paper we consider the following varying coefficient mixed-effects model:
$y_{ij}=z_{ij}^{\tau}b_{i}+x_{ij}^{\tau}\beta(w_{ij})+\xe_ij},\;i=1,\cdots,m; \;j=1,\cdots,n_i$, where $b_{i}$ is i.i.d. random effects with mean vector $\theta$ and covariance matrix $\sigma_{b}^{2}I_{q}$, $\xe_{ij}$ is i.i.d. random errors with zero mean and finite variance. The local polynomial estimator of the function coefficient vector $\beta(\cdot)$ is proposed. The method for estimating the mean of random effects, variances of random effects and random errors are also given. Asymptotic normality and consistency for the estimators are established, which give useful insight into the reliability of these general estimation methods.
• 学术论文
Qin Guoyou,Zhu Zhongyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(3): 320-326.
There are many nonparametric estimation methods for the mean functions of marginal models for longitudinal data. Those estimators such as regression spline, smoothing spline and seemingly unrelated(SUR) kernel estimators can achieve the minimum asymptotic variance when the true covariance structure is specified. The asymptotic bias of the regression spline estimator does not
depend on the working covariance matrix, but the asymptotic bias of smoothing spline and SUR kernel estimators depend on the working covariance matrix in a complicate manner. In this paper, we focus on the comparison of the estimation efficiency among the regression spline, smoothing spline and SUR kernel estimators. By simulation study, it is found that the regression spline estimator generally present higher efficiency than the other two estimators with smaller
mean square errors.
• 论文
LAO Yuan, ZHANG Shanguo, XUE Hongqi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 288-294.
In this paper, we study quasi-likelihood equation $\tsm_{i=1}^nX_i(y_i-\mu(X_i'\beta))=0$　for multivariate generalized linear models (GLMs). Under mild conditions, we prove the　asymptotic existence of the solution $\wh{\beta}_n$ to the above equation and present　its convergence rate, that is $\wh{\beta}_n-\beta_0=O_p(\underline{\lambda}_n^{-1/2})$,　where $\beta_0$ is the true value of parameter $\beta$ and $\underline{\lambda}_n$　denotes the smallest eigenvalue of the matrix $S_n=\tsm_{i=1}^nX_iX_i'$.
• 学术论文
Fan Junhua, Lin Jinguan, Wei Bocheng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(1): 12-26.
In longitudinal data analysis, homogeneity of variance is a basic assumption. However, this assumption is not necessarily appropriate. Lin and Wei[1] considered the tests for homogeneity of within-individual variances and between-individual autocorrelation coefficients in nonlinear models with AR(1) errors based on longitudinal data. This paper discusses the tests for homogeneity of variances and correlation coefficients in longitudinal data model with uniform correlation covariance structure and obtains several score test statistics. The glucose data is used to illustrate our results. Power simulations of the proposed tests are given in this paper.
• 学术论文
Lu Shulong, Liu Wenli
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 621-630.
Least square estimator (LSE) is disturbed easily by singular point; least absolute deviation estimator (LADE) can overcome the influence of singular point, but it is difficult in calculation. A convergent algorithm for LADE based on the stable
pole theorem of LADE under non-degenerate model is obtained in this paper. The progress of algorithm and comparison of linear programming are derived. Further this algorithm makes LADE more effective.
• 学术论文
CHEN Xia
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 337-346.
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.
• 学术论文
Zhao Lincheng, Wu Xiaoyan,Yang Yaning
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(4): 407-420.
Linear hypotheses in linear models can be tested by the M-method. The M-test, the Wald-type test (W-test) and the Rao's score-type test (R-test) are the three most commonly used testing methods. However, the critical values for these tests are usually related to the unknown error distribution. In this paper, we propose random weighting resampling methods for approximating the null distribution of these tests. It is shown that under both the null and the local alternatives these random weighting test statistics all have the same asymptotic null distributions as that for the original test statistic. The critical values of these tests can therefore be obtained by the Monte Carlo random weighting method. An important feature of the proposed methods is that the approximation are valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives. We conduct extensive simulations under different error distribution
specifications and different choices of random weighting variables to assess performance of proposed method. The results show that the random weighting M-testing method can provide pretty accurate approximation of the null distribution.
• 学术论文
Bao Wenqing
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 12-20.
To deal with optimal selection for empirical distribution, we propose mean square distance'' by introducing square loss function, and derive a new'' empirical distribution function, which is shown to be optimal. For comparisons of five empirical distribution functions, we adopt another measure in the sense of
Minimax'', and simulation is used to illustrate the domination of the new'' empirical distribution function in continuous population.
• 论文
SU Chun, MIAO Baiqi, FENG Qunqiang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 304-310.
The subtrees of various sizes and patterns in random binary search trees are
investigated in this paper. The expectations and variances of their numbers are
first derived from an essential recursive distributional equation. Applying the
contraction method, we show both of their asymptotic distributions are normal.
• 学术论文
XU WANGLI, LI ZAIXING
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 179-187.
Partially linear models are assumed to be linearly related to one or more variable,
but the relation to an additional variable or variables is not assumed to be easily
parameterized. One primary approach to estimate the parameter and nonparametric part is the method of penalized least squares method, generalized cross-validation (GCV) approach is a popular method for selecting the smoothing parameters. However, the optimality of GCV in the partial linear model with penalized least squares has not been proved. In this article, we provide the support for using GCV through its optimality of the smoothing parameter. Simulation studies are employed to investigate the empirical performance of generalized cross-validation and that of cross-validation for comparison in the context.

• 综合报告
Zhang Jianfang,Wang Xiuxiang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 201-214.
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.
• 学术论文
Su Yan,Yang Zhenghai
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(3): 234-244.

The $\chi^{2}$ conditional test for
multivariate normality is suggested. The transformed sample
$\mathbf{Y}_{d}=R\mathbf{V}_{d}$ from a $d$-variate normal
distribution has a symmetric multivariate Pearson type II
distribution, the result that $R^{2}$ has a beta distribution is
proved, the asymptotic Chi squared distribution of the statistic
$\chi^{2}$ based on beta distribution and sphere uniform
distribution is obtained. The Monte Carlo power study for
multivariate normality suggests that our test is a powerful
competitor to existing tests. The goodness-of-fit for multivariate
normality of iris data is analyzed.

• 论文
WU Changchun, ZHANG Runchu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 401-409.
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.
• 论文
DENG Wenli, ZHENG Zukang
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 419-428.

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.

• 学术论文
ZhangWeiming, Ahong Yunnan, Liu Jianbin
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(3): 265-272.
The paper provides estimators of process capability indices and their confidence
intervals based on $m$ subsamples, each of size $n$, discuss their properties,
presents the approximate sampling distributions and confidence intervals for some
indices.
• 学术论文
Li Gaorong,Feng Sanying,Xue Liugen
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(2): 190-206.
In this paper, the single-index model
for longitudinal data is considered, three empirical log-likelihood
ratio statistics for the unknown parameters in the model are
suggested to accommodate the independence of different subjects for
longitudinal data. It is proved that the proposed statistics are
asymptotically chi-square distribution under some suitable
conditions, and hence they can be used to construct the confidence
regions of the parameters. Furthermore, it is shown that the bias
corrected empirical log-likelihood ratio shares some desired
features. A simulation study is conducted to illustrate our
methods.
• 论文
FANG Zhaoben, HU Taizhong, WU Yaohua, ZHUANG Weiwei,
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 295-303.
In this paper, we investigate conditions on the underlying distribution function
and the parameters on which the generalized order statistics are based, to obtain　stochastic comparisons of spacing vectors of generalized order statistics in the　multivariate likelihood ratio and the usual multivariate stochastic orders. Some　applications of the main results are also given.
• 论文
Wang Songgui
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(3): 263-272.
This paper gives a survey of the recent developments on parameter estimation in linear mixed model. The covariance matrix in balanced analysis of variance mixed linear models has a specific structure. For this model, [1] proposed a new approach, spectral decomposition method, to estimate parameters. The merits of the approach is to provide independent estimates of fixed effects and variance components simultaneously, the former is linear and late quadratic. [2--9] established some further properties of the new estimates and corresponding estimates of covariance matrix with risk function. These papers also obtained some relations among the analysis of variance estimate, maximum likelihood estimate, restricted maximum likelihood estimate, minimum norm quadratic unbiased estimate and new estimates. Finally, some open problems are proposed.
• 论文
FEN Yu
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 365-371.
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.
• 论文
DING Zhaopeng
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 372-386.
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.
• 学术论文
Cui Henjian, Chan Laikow
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 113-122.
In this paper, a short production run process and some kinds of existed
control charts for short run process are introduced which includes plotted
statistics and control limits for subgroup and individual cases respectively.
Some comparisons are also addressed.
• 学术论文
Zhang Hao, Zhu Zhongyi
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(2): 171-184.
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.
• 论文
LIU Li, ZHU Liping
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2006, 22(4): 410-418.
$$x(t)+\int_t^Tf(s,x(s),y(s))\mbox{d}s+\int_t^Tg(s,x(s),y(s))\mbox{d}W(s)=\xi, \qq 0\leq t\leq T,$$where $W$ is a $d$-dimensional standard Wiener process. The existence and uniqueness