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

作　　者：魏亮瑜[1] 凌能祥[1] 李成好[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2012年第4期557-562,共6页Journal of Hefei University of Technology：Natural Science

基　　金：教育部人文社科规划基金资助项目(10YJA910005);安徽省自然科学基金资助项目(11040606M03)

摘　　要：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

关 键 词：函数型数据 相合性 遍历过程 鞅差 条件累积分布函数 条件分位数估计 

分 类 号：O212.7[理学—概率论与数理统计]