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Balanced augmented empirical likelihood for regression models
Xiaochao Xia,Zhi Liu 한국통계학회 2019 Journal of the Korean Statistical Society Vol.48 No.2
This paper studies the problem of convex hull constraint in conventional empirical likelihood. Specifically, in the framework of regression, a balanced augmented empirical likelihood (BAEL) procedure through adding two synthetic data points is proposed. It can be used to resolve the under-coverage issue, especially in small-sample or high-dimension setting. Furthermore, some asymptotic properties for proposed BAEL ratio statistic are established under mild conditions. The proposed approach performs robust to different random errors by choosing a robust loss function. Extensive simulation studies and a real example are carried out to support our results.
Hu Yang,Xiaochao Xia 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.1
This paper considers two tests on varying coefficient partially linear errors-in-variablesmodels (VCPLM-EV) with missing responses under the linear constraint. The restricted estimatorfor the parametric component is derived and proven to share asymptotically normaldistribution. In order to test the linear constraint, two statistics based on the profile Lagrangemultiplier method and the corrected residual sum of squares method respectively,are proposed. It is of interest to obtain that the magnitudes of the two statistics are equal exactlyand follow the asymptotical chi-square distribution. This reveals a new type of Wilk’sphenomenon in VCPLM-EV models with missing response. Finally, some numerical examplesare carried out to illustrate relevant performances.
Robust estimation and variable selection in censored partially linear additive models
Huilan Liu,Hu Yang,Xiaochao Xia 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.1
In this paper, we consider a new estimation in censored partially linear additive models in which the nonparametric components are approximated by polynomial spline. For identifying the significant variables in the linear part, a regularization procedure based on adaptive lasso is proposed for estimation and variable selection simultaneously. Under some regular conditions, the asymptotic normality and oracle property of the parametric components are established, and the convergence rates of the nonparametric components are obtained. Simulation studies and a real data analysis are presented to illustrate the behavior of the proposed estimators.