Abstract

This talk considers a new methodology for testing the parametric forms of the mean and variance functions based on weighted residual empirical processes and their martingale transformations in regression models. The dimensions of the parameter vectors can be divergent as the sample size goes to infinity. We study the convergence of weighted residual empirical processes and their martingale transformation under the null and alternative hypotheses in diverging dimension settings. The proposed tests based on weighted residual empirical processes can detect local alternatives distinct from the null at the fastest possible rate of order n^(−1/2) but are not asymptotically distribution-free. While tests based on martingale transformed weighted residual empirical processes can be asymptotically distribution-free, yet, unexpectedly, can only detect the local alternatives converging to the null at a much slower rate of order n^(−1/4), which is somewhat different from existing asymptotically distribution-free tests based on martingale transformations. As the tests based on the residual empirical process are not distribution-free, we propose a smooth residual bootstrap and verify the validity of its approximation in diverging dimension settings. Simulation studies and a real data example are conducted to illustrate the effectiveness of our tests.

报告人简介

• 北京师范大学珠海校区学术评议组（理科）组长，统计与数据科学研究中心首席专家，北京师范大学统计学院教授委员会主席。香港浸会大学特聘讲座教授，重要研究人员（featured researcher）。

• 美国科学促进会(AAAS),美国统计学会(ASA)，以及美国数理统计研究院(IMS) fellow 和国际统计研究院(ISI) elected member。

• 分别于1989年，2014年获国家教委科学技术进步二等奖和中国教育部自然科学奖二等奖；2013年度国家自然科学奖二等奖（独立获奖人）。1998年获德国洪堡研究奖（中国自然科学领域第一位获奖者，亚洲统计学界唯一获奖者）；国家重大人才计划入选者。1997年获国家基金委杰出青年基金，1999年获中国科学院百人计划支持。1995-96年度国家“百千万人才工程” 入选者。