基于遍历函数型数据条件分位数估计的相合性

Consistency of conditional quantile estimation for functional ergodic data

文章利用鞅的方法研究了基于平稳遍历函数型数据条件分位数的非参数估计,在一定的条件下建立了条件分位数估计的相合性,即在遍历数据集下,研究解释变量X取值于某半度量空间而响应变量Y取值于实值空间R时条件分位数的性质;同时给出了相同条件下条件分布函数的相合性和渐近性质,推广了现有文献中的相关结果。

In this paper, the nonparametric conditional quantile estimation for the functional stationary ergodic data is investigated by using the martingale approach, and the consistency of the estimator un- der certain conditions is established. More precisely, in the ergodic data setting, the property of con- ditional quantile is considered when the explanatory variable X takes values in a certain semi-metric abstract space and so is the response variable Y in real-value space R. The asymptotic property and the consistency of conditional distribution function are existing references. also given, which extend the related results in the