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讲座简介：
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In this talk, I will introduce a new metric, the so-called martingale difference correlation to measure the conditional mean dependence between a scalar response variable V and a vector predictor variable U. Our metric is a natural extension of the recently proposed distance correlation, which is used to measure the dependence between V and U. The martingale difference correlation and its empirical counterpart inherit a number of desirable features of distance correlation and sample distance correlation, such as algebraic simplicity and elegant theoretical properties. We further use martingale difference correlation as a marginal utility to do high dimensional feature screening to screen out variables that do not contribute to conditional mean of the response given the covariates. An extension to conditional quantile screening will be described and sure screening consistency for both screening procedures will also be presented. I will conclude the talk by showing selected simulation results and a real data illustration, which demonstrate the effectiveness of martingale difference correlation based screening procedures in comparison with the existing counterparts. |
