A0599
Title: A robust integrated mean variance correlation and its use in high dimensional data analysis
Authors: Wei Xiong - University of International Business and Economics (China) [presenting]
Abstract: A robust measure of independence is proposed between two random variables, named integrated mean-variance correlation (IMVC). It has several appealing properties, (a) it lies between zero and one, is zero if and only if the variables are independent and is one if and only if one variable is a measurable function of the other, (b) it is invariant to monotone transformations and is robust to the presence of outliers, (c) it is able to measure the degree of any functional dependencies, including both global and local dependence, (d) its estimation does not require moment conditions on both variables and has a relative low computational complexity. Several important applications of IMVC are considered. First, a distribution-free IMVC independence test is developed, and its explicit asymptotic null distribution is derived, which facilitates the fast calculation of p-values. Second, the IMVC is utilized as a marginal utility to identify active predictors in a high dimensional setting by introducing an IMVC-based model-free feature screening method. This framework can naturally handle censored data arising in survival analysis. To further control the false discovery rate, an IMVC-based local false discovery rate method is proposed that simultaneously exploits commonalities and heterogeneities among predictors, thus improving upon existing methods. The superior performance of the proposed procedures is demonstrated by exhaustive simulation examples and real data applications.
