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半距离相关及其应用AI 解读

We propose a new measure of dependence between a categorical random variable and a random vector with potentially high dimensions, named semi-distance correlation. It is an interesting extension of distance correlation to accommodate the information of the categorical random variable. It equals zero if and only if the categorical random variable and the other random vector are independent. Two important applications of semi-distance correlation are considered. First, we…

利用重新拟合交叉验证方差估计检验高维回归系数AI 解读

Testing a hypothesis for high-dimensional regression coefficients is of fundamental importance in the statistical theory and applications. In this paper, we develop a new test for the overall significance of coefficients in high-dimensional linear regression models based on an estimated U-statistics of order two. With the aid of the martingale central limit theorem, we prove that the asymptotic distributions of the proposed test are normal under two different distribution…