加权经验累计分位函数的弱收敛(英文)

Weak Convergence of Weighted Empirical Cumulative Quantile Regression Functions

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)=integral from n=0 to u(J(t)h(t)dt)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。

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.