The Statistics Seminar Speaker for Wednesday, April 6, 2016, is Yang Feng, an assistant professor of Statistics at Columbia University. His research interests include High-dimensional statistical learning, nonparametric and semiparametric methods, bioinformatics and network models. He got his Ph.D. from the Department of Operations Research & Financial Engineering (ORFE) at Princeton University under the supervision of Professor Jianqing Fan in 2010. Before that, he received his B.S. in Mathematics from the Special Class for the Gifted Young (SCGY), University of Science and Technology of China (USTC) in 2006.
Title: Model Selection in High-Dimensional Misspecified Models
Abstract: Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed dimensions. Yet model misspecification and high dimensionality are common in real applications. In this paper, we investigate two classical Kullback-Leibler divergence and Bayesian principles of model selection in the setting of high-dimensional misspecified models. Asymptotic expansions of these principles reveal that the effect of model misspecification is crucial and should be taken into account, leading to the generalized AIC and generalized BIC in high dimensions. With a natural choice of prior probabilities, we suggest the generalized BIC with prior probability which involves a logarithmic factor of the dimensionality in penalizing model complexity. We further establish the consistency of the covariance contrast matrix estimator in a general setting. Our results and new method are supported by numerical studies.
Refreshments will be served after the seminar in 1181 Comstock Hall