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The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors

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Science China Mathematics 2002年第2期45卷 137-146页

作者：胡舒合 1. Department of Mathematics Anhui University 230039 Hefei China

We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.

关键词： nonlinear regression model, dependent error, least squares estimator, strongconsistency rate.

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

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Science China Mathematics 2002年第7期45卷 845-858页

作者：吴启光杨国庆 1. Institute of Systems Science Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.

关键词： uniformly minimum risk equivariant estimator, affine group of transformations, quadratic loss, matrix loss.

On Bayes linear unbiased estimation of estimable functions for the singular linear model

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Science China Mathematics 2005年第7期48卷 898-903页

作者： ZHANG Weiping WEI Laisheng Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China

The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under m... 详细信息

关键词： singular linear model, Bayes LUE, best linear unbiased estimator, MSEM criterion.

A new method for the fast simulation of models of highly dependable Markov system

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Science China(Technological Sciences) 2005年第1期48卷 23-30页

作者： XIAO Gang LI Zhizhong Department of Industrial Engineering Tsinghua University Beijing 100084 China Department of Industrial Engineering Tsinghua University Beijing 100084 China

To fast evaluate the small probability that starts from the all-components-up state, the system hits the failed sets before returning to the all-components-up state, Important Sampling or Important Splitting is used commonly. In this paper, a new approach distinguished from Important Sampling and Important Splitting is presented to estimate this small probability of highly dependable Markov system. This new approach achieves variance reduction through improving the estimator itself. The new estimator is derived from the integral equation describing the state transitions of Markov system. That the variance of this estimator is less than that of naive simulation at all time is proved theoretically. Two example involved reliability models with deferred repair are used to compare the methods of RB, IGBS, SB-RBS, naive simulation, and the method presented in this paper. Results show our method has the least RE.

关键词： statistical estimator, variance reduction, dependability measures, Markov system, integral equation.

Strong convergence of LAD estimates in a censored regression model

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Science China Mathematics 2005年第2期48卷 155-168页

作者： FANG Yixin JIN Man ZHAO Lincheng Department of Statistics and Finance University of Science and Technology of ChinaHefei 230026China Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei 230026China Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei 230026China

A regression model with a nonnegativity constraint on the dependent variable,known as censored median regression model, is considered. Under some mild conditions, the LAD estimate of the regression coefficient is show...

关键词： censored regression, LAD estimator, strong consistency, convergence rate, Bahadur representation.

The asymptotic distributions of the statistics of the skew elliptical variables

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Science China Mathematics 2005年第2期48卷 214-221页

作者： FANG Biqi Institute of Applied Mathematics Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100080China

In this paper, the asymptotic properties of the quadratic forms and the T statistic of the skew elliptical variables are studied. Consistent estimators of some parameters are obtained. The robustness of the significan... 详细信息

关键词： skew elliptical distribution, asymptotic distribution, consistent estimator, hypothesis testing.

Central limit theorem of linear regression model under right censorship

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Science China Mathematics 2003年第5期46卷 600-610页

作者：何书元黄香 MAM and School of Mathematical Sciences. Peking University Beijing 100871 China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China Correspondence should be addressed to He Shuyuan

In this paper, the estimation of joint distribution F(y,z) of (Y, Z) and the estimation in thelinear regression model Y = b′Z + ε for complete data are extended to that of the right censored data. Theregression parameter estimates of b and the variance of ε are weighted least square estimates with randomweights. The central limit theorems of the estimators are obtained under very weak conditions and the derivedasymptotic variance has a very simple form.

关键词： asymptotic normality, linear regression, product limit estimator, right censoring,weighted least squares.

LAD estimation for nonlinear regression models with randomly censored data

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Science China Mathematics 2005年第7期48卷 880-897页

作者： ZHOU Xiuqing WANG Jinde School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China Department of Mathematics Nanjing University Nanjing 210093 China Department of Mathematics Nanjing University Nanjing 210093 China

The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.

关键词： randomly censored data, nonlinear regression model, LAD estimator, asymptotic normality.

On asymptotics of t-type regression estimation in multiple linear model

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Science China Mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of Mathematics, Beijing Normal University, Beijing 100875, China 1. Department of Mathematics Beijing Normal University 100875 Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.