Local Influence Detection of Conditional Mean Dependence

Abstract

This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable. A local influence detection approach is developed combining with the martingale difference divergence (MDD) metric, and an efficient wild bootstrap implementation is given. The obtained new metric of the conditional mean dependence holds the merits of MDD, while it is more sensitive than the original one, and leads to a powerful test to nonlinear relationships. It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings. Theoretical asymptotic properties of the local influence test statistic are given, and a real data analysis is also presented for further illustration. The localization idea could be combined with other conditional mean dependence metrics.