报告题目：Inference for Possibly Misspecified Generalized Linear Models with Non-Polynomial
Dimensional Nuisance Parameters
报告人：蒋建成 北卡罗来纳大学夏洛特分校
报告时间：2024年6月4日(周二) 16:30-18:00
报告地点：中国科学院数学与系统科学研究院南楼N204
腾讯会议ID：473 996 879
内容摘要
It is a routine practice in statistical modelling to first select variables and then make inference for the selected model as in stepwise regression. Such inference is made upon the assumption that the selected model is true. However, without this assumption, one would not know the validity of the inference. Similar problems also exist in high dimensional regression with regularization. To address these problems, we propose a dimension-reduced generalized likelihood ratio (DR-GLR) test for generalized linear models with non-polynomial dimensionality, based on the quasi-likelihood estimation which allows for misspecification of the conditional variance. The test has nearly oracle performance when using the correct amount of shrinkage and has robust performance against the choice of regularization parameter across a large range. We further develop an adaptive data-driven DR-GLR test and prove that with probability going to one it is an oracle GLR test. However, in ultrahigh-dimensional models the penalized estimation may produce spuriously important variables which deteriorate the performance of test. To tackle this problem, we introduce a cross-fitted DR-GLR test, which is not only free of spurious effects but robust against the choice of regularization parameter. We establish limiting distributions of the proposed tests. Their advantages are highlighted via theoretical and empirical comparisons to some competitive tests. Extensive simulations demonstrate more favorable finite sample performance of the proposed tests. An application to breast cancer data illustrates the use of our proposed methodology.
主讲人简介
