加权经验累计分位函数的弱收敛
Weak Convergence of Weighted Empirical Cumulative Quantile Regression Functions
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摘要: 记(X,Y)为二元随机变量,F(x)为X的边缘分布函数,定义Y关于X的分位回归函数为h(u)=E(Y|F(X)=u),记S(u)=\int_0^u J(t) h(t) \mathrmd t为加权累计分位回归函数,其中J(·)为权函数,本文讨论了S(u)的经验版本的弱收敛性质。Abstract: Let (X, Y) be a bivariate random variable and F(x) the marginal distribution function of X. We define h(u) = E(Y|F(X) = u) as the quantile regression (QR) function of Y on X. The Cumulative QR function S(u) with weighted coefficients is defined as the integral of J(·)h(·) over the range O,u, where J(·) is the weight function. In this paper, we discuss the convergence properties of its empirical versions.