Prof. Xu Guo 郭旭教授
Beijing Normal University
Adaptive adequacy testing of high-dimensional factor-augmented regression model
Abstract 摘要
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression models. For independent observations, we first propose a maximum-type statistic for detecting sparse alternatives and establish its Gumbel limiting distribution. To improve power against dense alternatives, for which maximum-type procedures generally do not perform well, we introduce a novel quadratic-type test statistic and establish its asymptotic normality. The two proposed test statistics are robust to heteroscedastic errors. For temporally dependent observations, we develop bootstrap-calibrated maximum-type and quadratic-type tests tailored to sparse and dense alternatives, respectively. We establish the validity of the bootstrap-calibrated maximum-type test and also characterize its power properties. The theoretical results for the maximum-type procedure allow for both heteroscedastic errors and polynomial-tailed distributions. Since the sparsity structure of the alternative is typically unknown, we establish the asymptotic independence of the two test statistics for independent observations and construct an adaptive test procedure based on Fisher's combination method. The combined procedure attains favorable power under both sparse and dense alternatives. Simulation studies and an empirical application to the Federal Reserve Economic Data-Monthly Database demonstrate the finite-sample performance and practical relevance of the proposed procedures.
Speaker Biography 讲者简介
Xu Guo, Professor and PhD Supervisor, School of Statistics, Beijing Normal University. His research interests include hypothesis testing for high-dimensional regression models and statistical inference with machine learning algorithms. He has published papers in top international journals in statistics and econometrics, such as JRSSB, JASA, Biometrika, JOE and JMLR. He serves as Associate Editor of *Journal of Multivariate Analysis* (IMVA), and a member of the 10th editorial board of *Chinese Journal of Applied Probability and Statistics*. He is the principal investigator of the NSFC Excellent Young Scientists Fund (Type B). His teaching awards include the 11th "Top Ten Teachers Most Popular with Undergraduates" of BNU, first prize in the 18th BNU Young Teachers Teaching Competition, and third prize in the 13th Beijing Young Teachers Teaching Competition.
Topics 涉及主题
Sparse & dense robust tests Fisher adaptive combination test Bootstrap for dependent data