A0801
Title: Measuring multivariate regression association via spatial signs
Authors: Jia-Han Shih - National Sun Yat-sen University (Taiwan) [presenting]
Yi-Hau Chen - Academia Sinica (Taiwan)
Abstract: A regression association measure is proposed, aiming at the predictability of a multivariate outcome ${\bf Y} = (Y_1, . . . , Y_d)$ from a multivariate covariate ${\bf X} = (X_1, . . . ,X_p)$. Motivated by existing measures, Kendall's tau is first generalized to measure the association between two random vectors. The generalized Kendall's tau of two independent replications, $\bf Y$ and $\bf Y'$, is then used from the conditional distribution of $\bf Y$ given $\bf X$, to measure the predictability of $\bf Y$ from $\bf X$. The proposed regression association measure can be expressed as the proportion of the variance of some function of $\bf Y$ that can be explained by $\bf X$, indicating that the measure has a direct interpretation in terms of predictability. Based on the proposed measure, a conditional regression association measure is further defined, which can be utilized to perform variable selection. Since the measure is constructed based on two independent replications from the conditional distribution, a simple nonparametric estimation method based on the nearest neighbor is available. Simulations are carried out to examine the performance of the proposed variable selection algorithm, and real data examples are analyzed for illustration.
