Statistical inferential methods are used to answer questions in a variety of modern science disciplines. For example, in medical studies, whether the treatment effect varies by different individuals and which treatment procedure will be recommended to a future patient given his or her baseline information; in genomics, whether different traits share common genetic etiology and how gene expression levels are regulated by genetic variants. For these complex studies, high-dimensional linear models have become ubiquitous to approximate the data generating mechanism and extract useful information. Despite significant advances on estimation, inference problems in high-dimensional linear models have been far less understood, from both methodological and theoretical perspectives. In this project, the investigator plans to address the methodological and theoretical challenges of high-dimensional statistical inference problems, including confidence interval construction and hypothesis testing, and apply the developed methods to answer important scientific questions encountered in genomics and health studies.
The research objective is to construct confidence intervals and conduct hypothesis testing in a simultaneous consideration of multiple sparse high-dimensional linear models, which are important in answering scientific questions encountered in a wide range of applications. Specifically, the investigator will tackle statistical inference problems by the following means: (1) constructing confidence intervals for functionals of multiple regression vectors and conduct significance tests for groups of variables; (2) testing the existence of heterogeneity in treatment effects and compare efficacy of different treatment procedures for a specific individual; (3) studying multiple testing procedures for a large number of functionals; and (4) applying the developed inferential procedures and collaborate with researchers in genomics and epidemiology to answer important scientific questions about genetic relatedness network and personalized treatment comparison through analyzing large-scale data sets.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
