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Sharp Error Estimate for Maximum Likelihood Estimator of Nonstationary Diffusion Processes

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Acta Mathematica Sinica,English Series 2005年第2期21卷 303-314页

作者： ZhiYanXU WeiAnZHENG departmentofstatistics EastChinaNormalUniversityShanghai200062P.R.China departmentofstatistics EastChinaNormalUniversityShanghai200062P.R.ChinaDepartmentofMathematicsUniversityofCaliforniaIrvineCA92697USA

We consider the maximum likelihood estimator of the unknown parameter in aclass of nonstationary diffusion processes. We give further a precise estimate for the error of theestimator.

关键词： stochastic differential equation diffusion processes maximum likelihoodestimator

Bootstrap Approximation to the Distribution of M-estimates in a Linear Model

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Acta Mathematica Sinica,English Series 2004年第1期20卷 93-104页

作者： XiaoMingWANG WangZHOU departmentofstatistics ShanghaiUniversityofFinanceandEconomicsShanghai200433P.R.China DepartmentofMathematics HongKongUniversityofScienceandTechnologyHongKong

The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.

关键词： Linear model M-estimate Linear representation Bootstrap approximation Normal approximation Randomly weighted approximation

DISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATADISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATA

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Chinese Annals of Mathematics,Series B 2000年第4期21卷 489-498页

作者： WANGXIAOMING ZHAOLINCHENG WUYAOHUA departmentofstatistics ShanghaiUniversityofFinanceandEconomicsShanghai200433China. departmentofstatisticsandFinance UniversityofScienceandTechnologyofChinaHefei230026China.

The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of desig... 详细信息

关键词： Directional data Laws of the iterated logrithm Regression function kernel estimator Strong convergence rates

A Generalized Information Criterion for Parameters under an Umbrella Order Restriction

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Northeastern Mathematical Journal 2005年第2期21卷 127-130页

作者：宋海燕陶剑史宁中 InstituteofMathematics JilinUniversityChangchun130012／／DepartmentofStatisticsNortheastNormalUniversityChangchun130024 departmentofstatistics NortheastNormalUniversityChangchun130024 不详

The detection of the configuration of parameters is one of the most important problems in statistical studies. It is well known that the Akaike’s information criterion (AIC) is a key tool for this problem

关键词： umbrella ordering level probability AIC criterion ORIC criterion

Detecting Change Points in Polynomial Regression Models with an Application to Cable Data Sets

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Acta Mathematicae Applicatae Sinica 2004年第4期20卷 541-546页

作者： Yin-caiTang He-liangFei departmentofstatistics EastChinaNormalUniversityShanghai200062China DepartmentofAppliedMathematics ShanghaiNormalUniversityShanghai200234China

In this paper, the Schwarz Information Criterion (SIC) is used to detect the change points in polynomial regression models. Switching quadratic regression models with same amount of model deviation and switching polynomial regression models with different amount of model deviation for different segments of regression are considered. The number of separate regimes and their corresponding regression orders are assume to be known. The method is then applied to cable data sets and the change points are successfully detected.

关键词： Information criterion change points polynomial regression models

Gelation of a Reversible Markov Process of Polymerization

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 87-96页

作者： DongHan Yian-linHan DepartmentofMathematics ShanghaiJiaoTongUniversityShanghai200030China departmentofstatistics XinjiangFinanceUniversityUrumqi830000China

Abstract In this paper a reversible Markov process as a chemical polymers reaction of two types of monomers is defined. By analyzing the partition functions of the process we obtain three different distributions of the average molecular weight, depending on the value of strength of the fragmentation reaction, and prove that a gelation of the process will occur in the thermodynamic limit.

关键词： Keywords Polymer reversible Markov process gelation average molecular weight

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

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Acta Mathematicae Applicatae Sinica 2005年第2期21卷 257-268页

作者： Xing-weiTong Heng-jianCui HuiZhao DepartmentofMathematics BeijingNormalUniversityBeijing100875China departmentofstatistics CentralChinaNormalUniversityWuhan430079Chin

For partial linear model Y = X~τβ_0 + g_0(T) + ε with unknown β_0 ∈ R^dand an unknown smooth function g_0, this paper considers the Huber-Dutter estimators of β_0, scaleσ for the errors and the function g_0 respectively, in which the smoothing B-spline function isused. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σ areasymptotically normal with convergence rate n^(-1/2) and the B-spline Huber-Dutter estimator of g_0achieves the optimal convergence rate in nonparametric regression. A simulation study demonstratesthat the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameterand the ordinary least square estimator. An example is presented after the simulation study.

关键词： Huber-dutter estimator partial linear model m-estimator optimalconvergence rate B-spline function

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

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Journal of Systems Science & Complexity 2003年第4期16卷 506-512页

作者： YUEDequan ZHANGHuachen TUFengsheng departmentofstatistics YanshanUniversityQinhuangdao066004China DepartmentofAutomation NankaiUniversityTianfin300071China

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.

关键词： markov chain transition probability matrix ATM network.

A KULLBACK-LEIBLER EMPIRICAL LIKELIHOOD INFERENCE FOR CENSORED DATA

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Journal of Systems Science & Complexity 2002年第1期15卷 77-84页

作者： SHIJian Tai-ShingLan InstituteofSystemsScience AMSSChineseAcademyofSciencesBeijing100080China departmentofstatistics TheChineseUniversityofHongKongShatinN.T.HongKongChina

In this paper, two kinds of Kullback-Leibler criteria with appropriate constraints are proposed to construct empirical likelihood confidence intervals for the mean of right censored data. It is shown that one of the c... 详细信息

关键词： Empirical likelihood Kullback-Leibler distance right censorship Kaplan-Meier estimator confidence interval.