Inference for possibly misspecified generalized linear models with non-polynomial dimensional nuisance parameters


报告人  Prof.  Jiancheng Jiang

Department of Mathematics and Statistics, University of North Carolina


主持人:谢广明  教授





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.


Dr. Jiancheng Jiang is Professor of Statistics in the Department of Mathematics and Statistics & the School of Data Science at the University of North Carolina (UNC) at Charlotte. He has published over 70 refereed research papers in (bio)statistics and financial econometrics  and been awarded several NSF/NIH/NSFC grants, in addition to serving as AE for several professional journals and as statistics program coordinator of his department for many years. His research interests include but not limited to AI-driven mathematics, financial time series, statistical inference for high-dimensional models, survival analysis, and nonparametric smoothing. Currently he serves as co-PI of the Charlotte Center for Trustworthy AI through Model Management (TAIM2) at UNC Charlotte.