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2009 Vol.25 Issue.3,Published 2009-05-20

学术论文
225 Ergodicity for Q-Processes with Markovian Switching
Xi Fubao
Exponential ergodicity and strong ergodicity for a form of Q-processes with Markovian switching are considered by virtue of the Foster-Lyapunov inequality and the coupling methods respectively. Meanwhile, some couplings of this form of Q-processes with Markovian switching are constructed, and a coupling is proved to be successful.
2009 Vol. 25 (3): 225-237 [Abstract] ( 1791 ) [HTML 0KB] [ PDF 232KB] ( 1390 )
238 A Method of Estimate of $\gamma^{2}$ for the Extrema of Conditional Sample Function

Wu Jianguo

ome methods of estimate of $\gamma^{2}$ in the conditional sample functions are discussed. A new method-bootstrap is putted forward and the properties of the statistics which are obtained from the new method are analyzed.
2009 Vol. 25 (3): 238-244 [Abstract] ( 1572 ) [HTML 0KB] [ PDF 205KB] ( 1265 )
245 Variable Selection in Joint Generalized Linear Models
Wang Darong,Zhang Zhongzhan
We focus on variable selection in this paper, and propose a variable selection criterion based on the extended quasi-likelihood which is for joint generalized linear models with structured dispersions. The new criterion is an extension of Akaike's information criterion. Its performance is investigated through simulation studies and a real data application.
2009 Vol. 25 (3): 245-256 [Abstract] ( 2472 ) [HTML 0KB] [ PDF 222KB] ( 1655 )
257 A Synthetic Control Chart Based on Cornish-Fisher\\Expansion
Wu Chunjie,Wang Zhaojun
According to Cornish-Fisher expansion, the control limits of Shewhart $\ol X$ control chart were constructed with up to the fourth moment (The moments are estimated from the in-control historical samples when the process distribution is
unknown, and no further assumptions are made on the distribution). Then we made a synthetic control chart based on the Cornish-Fisher expansion. The in-control ARL's (average run length) and out-of-control ARL's of the new chart builded here were evaluated to compare with synthetic control chart (see \cite{1}) when the process distribution is Student-t, Weibull, Lognormal and Burr. Simulation results show that the new control chart is more robust than the
other methods.
2009 Vol. 25 (3): 257-265 [Abstract] ( 1661 ) [HTML 0KB] [ PDF 226KB] ( 1340 )
266 Estimating the Monotonic Link Function in Single-Index Models
Yang Jianjuan
In this paper, we propose to estimate the monotonic link function of the single-index model by I-spline approximation. On the basis of a consistent estimation of the projection direction, the consistency of the least square criterion with a penalty function is established. Simulations are carried out to compare the existing method and to evidence the efficacy of our propose approach.
2009 Vol. 25 (3): 266-274 [Abstract] ( 1985 ) [HTML 0KB] [ PDF 229KB] ( 1521 )
275 Strong Law of Large Numbers of Absolute Value Sequences from Varying-Coefficient ARCH Models
Zhang Zhiqiang,Feng Jingyan
In this paper we introduce a varying-coefficient ARCH model in which the model coefficient is a function of time variable $t$. It is consistent with the fact that the coefficients are different in different time intervals in modeling, so this kind
of model is more reasonable. We believe that the varying-coefficient ARCH model has several potential advantages for practical uses, it is more flexible. Here we discuss the strong law of large numbers of absolute value sequences from varying-coefficient ARCH models.
2009 Vol. 25 (3): 275-280 [Abstract] ( 2093 ) [HTML 0KB] [ PDF 231KB] ( 1297 )
281 Some Properties of a Generalized Fractional Brownian Motion
Lin Zhengyan,Zheng Jing
In the paper, we give a new generalization of fraction Brownian motion (gfBm). We study the existence of the local nondeterminism and the joint continuity of the local time of gfBm, and we get upper and lower bounds of Hausdorff dimensions of the level sets of a gfBm.
2009 Vol. 25 (3): 281-289 [Abstract] ( 1840 ) [HTML 0KB] [ PDF 210KB] ( 1477 )
290 Estimating and Testing Parameter for Regression Credibility Model with Linear Trend
Tang Guoqiang,Department of Mathematics and Physics,Guilin University of Technology
In this paper, the parameters of regression credibility model with linear trend are estimated and tested. Orthogonal transformation is used to estimate parameter and unbiased estimate of parameters are obtained. Likelihood ratio test is used to test randomness and linear trend. The better P-value of likelihood ratio test is got and Monte-Carlo simulation is performed.
2009 Vol. 25 (3): 290-300 [Abstract] ( 1832 ) [HTML 0KB] [ PDF 274KB] ( 1374 )
301 Estimates of Variance Components in Linear Mixed Models with Random Effects
Xu Wangli
In this paper, we propose the improved ANOVA estimates for the linear mixed models with three variance components which are better than ANOVA estimators in the criteria of smaller mean square error (MSE). Based on the fact that the proposed variance estimators are not nonnegative with positive probability, we censor the proposed estimators in some points. Furthermore, we discuss the sufficient conditions to ensure the truncated estimators be nonnegative. The conclusions are extended to more general linear mixed models models with random effects.
2009 Vol. 25 (3): 301-308 [Abstract] ( 2200 ) [HTML 0KB] [ PDF 234KB] ( 1447 )
309 The Orthogonal Saturated Effects Model and Its Statistical Analysis
Zhang Xiaoqin,Li Shunyong
The paper proposes a new model, that is, the orthogonal saturated effects model, to analyze the general saturated design. In addition, the paper gives the LSE estimators and their properties of the unknown parameters in this model, and gives the decomposition of the sum of squares. At last, the
Procedure of Searching Zero Effects is used to test the active effects. The results of the simulated example shows that it is satisfied.
2009 Vol. 25 (3): 309-319 [Abstract] ( 1621 ) [HTML 0KB] [ PDF 272KB] ( 1218 )
320 The Comparison of Nonparamteric Smoothing Methods for Longitudinal Data
Qin Guoyou,Zhu Zhongyi
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.
2009 Vol. 25 (3): 320-326 [Abstract] ( 2865 ) [HTML 0KB] [ PDF 224KB] ( 1954 )
327 Statistical Analysis for Nonlinear Mixed Models with Random Design
Fang Yun,Wu Ping,Zhu Lixing
In this paper, we study point estimation and confidence interval construction for the parameters of interest in nonlinear mixed effects models with random times of repeated measurements for subjects. Under only moment conditions, we define the moment estimators of the fixed effects, the covariance matrix of
the random effects and the variance of the errors. The consistency and asymptotic normality of the estimators are obtained. To construct confidence intervals of the variances of the error and the random effects, we also estimate the fourth moments of the random effects and the errors. For illustrating the effect of our method, a simulation study is given.
2009 Vol. 25 (3): 327-336 [Abstract] ( 2208 ) [HTML 0KB] [ PDF 233KB] ( 1590 )
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