报告题目：Inference for ultra high-dimensional quasi-likelihood models based on data splitting

主讲人：蒋建成教授（美国北卡洛莱纳大学夏洛蒂分校）

时间：2023年7月18日（周二）16:00 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：

In this talk, we develop a valid framework for inference of ultra-high dimensional quasi-likelihood models, based on a novel weighted estimation approach. The weighted estimator is obtained by minimizing the variance function. We split the full data into two subsets and perform model selection on one subset while computing the maximum quasi-likelihood estimator on the other. The two estimators are then aggregated using optimal weighted matrices. Using the weighted estimator, we construct confidence regions for a group of components of the regression vector and perform the Wald test for a linear structure of the group components. Theoretically, we establish the asymptotic normality of the weighted estimator, and the asymptotic distributions of the Wald test statistic under the null and alternative, without assuming model selection consistency. We highlight the advantages of the proposed tests through theoretical and empirical comparisons with some competitive tests, which guarantees that our proposed inference framework is locally optimal. Furthermore, we prove that when selection consistency is achieved, the proposed Wald test is asymptotically identical in distribution to the oracle test which knows the support of the regression vector. We also demonstrate the superior finite sample performance of our proposed tests through extensive simulations. Finally, we illustrate the application of our methodology to a breast cancer dataset.

主讲人简介：

蒋建成博士现任美国北卡洛莱纳大学夏洛蒂分校统计学教授，曾在2017-2020兼任南开大学统计学讲席讲授。蒋教授曾担任北卡洛莱纳大学夏洛蒂分校统计项目负责人，2017年以来担任Statistica Sinica和其它数种期刊的副主编。2004年以来，他主持美国国家科学基金（NSF）和美国国立卫生研究院（NIH）多个项目。蒋教授的研究兴趣包括统计学（生物统计）、计量经济学和数据科学。