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Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

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Acta Mathematicae Applicatae Sinica 2003年第4期19卷 599-610页

作者： Jin-hong You gemai Chen Department of Biostatistics University of North CarolinaChapel HillNC 27599-7420U.S.A.Department of Mathematics & StatisticsUniversity of Calgary CalgaryAlbertaCanada T2N 1N4

Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You[23] proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].

关键词： Partially linear regression model asymptotic variance heteroscedasticity delete-group jackknife semiparametric generalized least squares estimator

Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 247-272页

作者： Bin ZHOU Jinhong YOU Qinfeng XU gemai CHEN School of Finance and Statistics East China Normal University Shanghai 200241 China. Department of Statistics Shanghai University of Finance and Economics Shanghai 200433 China. Corresponding Author. School of Management Fudan University Shanghai 200433 China. Department of Mathematics and Statistics University of Calgary Calgary Alberta T2N 1N4 Canada.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.

关键词： Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap

A NEW TEST FOR NORMALITY IN LINEAR AUTOREGRESSIVE MODELS

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Journal of Systems Science & Complexity 2002年第4期15卷 423-435页

作者： CHEN Min WU Guofu gemai Institute of Applied Mathematics Chinese Academy

A nonparametric test for normality of linear autoregressive time series is proposed in this *** test is based on the best one-step forecast in mean square with time *** asymptotic theory is developed for the test,and it is shown that the test is easy to use and has good *** empirical percentage points to conduct the test in practice are provided and three examples using real data are included.

关键词： Nonparametric test time-reversibility one-step forecast Kolmogorov-Smirnov statistic.

Hierarchical linear regression models for conditional quantiles

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Science China Mathematics 2006年第12期49卷 1800-1815页

作者： TIAN Maozai & CHEN gemai School of Statistics, Renmin University of China, Beijing 100872, China and Center for Applied Statistics, Renmin University of China, Beijing 100872, China Department of Mathematics and Statistics, University of Calgary, Canada School of Statistics Renmin University of China Beijing 100872 China Department of Mathematics Statistics University of Calgary Canada Center for Applied Statistics Renmin University of China Beijing 100872 China

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical *** practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common *** ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships *** the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max ***,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional ***,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent *** this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is *** the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic *** also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

关键词： hierarchical quantile regression models,EQ algorithm,fixed effects,random effects,regression quantile.

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

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Journal of Systems Science & Complexity 2004年第4期17卷 511-522页

作者： JinhongYOU CHENMin gemaiCHEN UniversityofRegina ReginaSaskatchewanS4S0A2Canada AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China UniversityofCalgary CalgaryAlbertaT2N1N4Canada

Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.

关键词： semiparametric regression model fixed-design asymptotic normality lineartime series errors