Semiparametric Inference for High-dimensional Correlated or Heterogeneous Cross-sectional Data with Discrete Response

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Substantial advancement has been achieved over the past decade in high-dimensional data analysis with diverging number of covariates. However, when the research interest is focused on modeling the relationship between the response variable and a high-dimensional vector of covariates, most existing work only applies when the response variable is continuous and often requires stringent conditions such as independence or homogeneity. Many fundamental problems remain unsolved for high-dimensional data with discrete responses, especially when the standard modeling assumptions are not satisfied. This project aims to develop new statistical theory, methodology and algorithms for analyzing high-dimensional correlated or heterogeneous cross-sectional data with binary or count responses. More specifically, the investigator will (1) rigorously study the asymptotic theory, including consistency and asymptotic normality, of the semiparametric procedure of generalized estimating equations in the new diverging p asymptotic framework; (2) investigate generalized estimating equations based variable selection procedures for high-dimensional longitudinal and spatially correlated data; and (3) investigate the theory and methodology of sparse quantile regression, where the number of parameters may greatly exceed sample size, for analyzing heterogeneous data with possibly discrete responses.The prevalence of high-dimensional binary and count data in various scientific fields, such as biomedical and health sciences, economics, social sciences and environmental studies, demands new statistical theory, methodology and software. Many important issues in analyzing high-dimensional binary or count data, especially in the presence of correlation or heterogeneity, have not been systematically studied. Moreover, existing work based on the full likelihood or the independence assumption in the high-dimensional setting cannot be readily applied. This project will make significant and timely contribution to the general theory and methodology of high-dimensional data analysis in the diverging p framework. Such theories are critical for guiding practical data analysis. Undergraduate and graduate students, especially those from underrepresented groups, will be encouraged to participate in this research project.