A0480
Title: Measuring multivariate regression association via spatial sign
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 Y from a multivariate covariate X. Motivated by existing measures, the usual Kendall's tau is first generalized to measure the association between two random vectors. The predictability of Y is then measured from X by the generalized multivariate Kendall's tau between two independent replications, Y and Y', from the conditional distribution of Y given X. The proposed regression association measure can be expressed as the proportion of the variance of a function of Y that can be explained by X, indicating that the measure has a direct interpretation in terms of predictability. Based on the 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 approach using the nearest neighbor is available. Simulation studies are carried out to assess the performance of the proposed methods, and real data examples are analyzed for illustration.
