Speaker: Liang Hanying, Professor, School of Mathematical Sciences, Tongji University

Date: Nov.15, 2021

Time: 16:00-17:00

Location: Tencent Meeting, ID:302 605 253

Sponsor: School of Mathematics, Shandong University

Abstract:

In this talk, we focus on empirical likelihood in high dimensional partially linear single-index quantile regression with observations missing at random. Applying B-spline approximation to unknown link function, we construct bias-corrected empirical likelihood ratio functions and define maximum empirical likelihood (MEL) estimators of the parameters, and establish asymptotic distributions of the empirical likelihood ratio functions and MEL estimators. Unlike existing empirical likelihood procedures for the partially linear single-index model with finite dimensional parameters, the bias-corrected empirical likelihood ratios no longer share the asymptotic Chi-Square distribution, but the asymptotic normality in high dimensional case. Moreover, based on penalized approach, selection consistency and asymptotic normality of variable selection are considered. Also, we propose a penalized empirical likelihood ratio statistic to test hypothesis. Simulation study is conducted to verify the performance of the proposed methods.

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https://www.view.sdu.edu.cn/info/1020/159049.htm