Abstract: My talk aims to introduce an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is chi-square distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power
analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed chi-square tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world data set is used to illustrate the proposed methodology.

https://science.psu.edu/stat/people/ril4