基于遍历函数型数据下条件分位数的渐近性质

Asymptotic property of conditional quantile for functional ergodic data

假设(Xi,Yi)1≤i≤N为一组平稳遍历函数型样本,Yi为取值于实数空间R的随机变量,Xi为取值于半度量空间F。文章考虑在Xi条件下关于Yi分位数回归函数的估计量,主要利用N-W核回归估计方法研究遍历函数型数据下条件分位数的逐点收敛速度。

Let（ Xi ,Y i ）1≤ i≤ N be a sequence of functional stationary ergodic processes ,Y i is a random variable val-ued in a real space R ,Xi is valued in a semi-metric space F .The problem of estimating the quantile regression function of Yi with Xi is considered .The method of N-W kernel regression estimation is used to study the pointwise convergence rate of the conditional quantile for functional stationary ergodic data .