|
Abstract:
|
In this article, we propose a general framework of independence measure with respect to statistical functionals of interest , which unifies some existing independent measures, such as distance covariance, Hilbert Schmidt independence criteria and martingale difference correlation. In particular, we propose a new metric, the martingale difference correlation with Reproducing Kernel to measure the conditional mean independence. In simulations and real data applications, the sample counterpart of the proposed metric can effectively select variables that marginally contribute to the mean of the response variable. To address the potential issue of missing important variables that have zero marginal utility with the response, we further propose a forward variable screening method. Under regularity conditions, it is able to select the variables that jointly but not marginally contribute to the mean of the response variable.
|
