Dissertation Defense by Haeun Moon

Monday, April 25th at 12:45 p.m.

Wesley W. Posvar Hall, Department of Statistics, Seminar Room

Title: A New Test of Independence and Its Application to Variable Selection

Abstract: In the first part of our research, we propose a new interpoint-ranking sign covariance measure for nonparametric test of independence. The proposed method is applicable to general types of random objects as long as a meaningful similarity measure can be defined, and it is shown to be zero if and only if the two random variables are independent. The test statistic is a $U$-statistic, whose large sample behavior guarantees that the proposed test is consistent against general types of alternatives. Numerical experiments and data analyses demonstrate the great empirical performance of the proposed method. In the second part, we propose to combine the frequency voting idea with the proposed and existing test of independence methods for model-free variable selection. This research is motivated and illustrated by an application in selecting important genes related to suicidal behavior. Numerical experiments demonstrate nice empirical performance of the proposed method.

Committee Chair and Advisor: Dr. Kehui Chen