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報告題目：Inference for ultra high-dimensional quasi-likelihood models based on data splitting

主講人：蔣建成教授（美國北卡洛萊納大學(xué)夏洛蒂分校）

時間：2023年7月18日（周二）16:00 p.m.

地點：北院卓遠(yuǎn)樓305會議室

主辦單位：統(tǒng)計與數(shù)學(xué)學(xué)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.

主講人簡介：

蔣建成博士現(xiàn)任美國北卡洛萊納大學(xué)夏洛蒂分校統(tǒng)計學(xué)教授，研究興趣包括統(tǒng)計學(xué)（生物統(tǒng)計）,、計量經(jīng)濟學(xué)和數(shù)據(jù)科學(xué),，曾在2017-2020兼任南開大學(xué)統(tǒng)計學(xué)講席講授,，曾擔(dān)任北卡洛萊納大學(xué)夏洛蒂分校統(tǒng)計項目負(fù)責(zé)人，2017年以來擔(dān)任Statistica Sinica和其它數(shù)種期刊的副主編,。2004年以來,，主持美國國家科學(xué)基金（NSF）和美國國立衛(wèi)生研究院（NIH）多個項目。