截尾样本下非参数回归函数改良分割估计的渐近正态性

Asymptotic normality of modified partitioning estimate of nonparametric regression function under censored sample

设{(Xi,Yi),i≥1}是从取值于Rd×R1的总体(X,Y)中抽出的一个i.i.d样本E|Y|<∞。文章在简洁的条件下,利用截尾数据的性质和鞅的有关理论,证明了非参数回归函数改良分割估计的渐近正态性。

Let {（Xi ,Yi） ,i≥1} be i. i. d random vectors taking values inRa×R1 with E｜Y｜〈∞. In this paper, based on censored samples, the asymptotic normality of modified partitioning estimate of nonparametric regression function is proved under suitable conditions by using the properties of censored data and martingale theory.