删失数据下回归函数的最近邻估计(英文)

Nearest Neighbor Regression Function Estimation with Censored Data

设（X，Y）是一随机向量且变量Y的均值存在．假定Y被另一分布G的随机变量t删失，仅能观察到不完全数据（xi，Yi^ti,δi），i＝1，2，…n，其中Yi^ti＝min（Yi，Ti）,δi=I（Yi≤ti）。为了给出回归函数m（x）＝E（Y|X）的估计。文中使用了Stute提出的最近邻型回归估计，并给出了该估计的强相合性结果．

Let (X, Y) be an R2 valued vector with E|Y| <∞. {Yi} are censored by random variables {ti} with d.f.G and the available observations are of the form (zi, δi, Xi), 1≤ i≤n, where Zi = Yi ti andδi = I(Yi ≤ ti). To estimate the regression function m(x0) = E(Y|X = x0),we propose a Stute's(1984) type estimator, i.e. the nearest neighbor regression estimator, when the data subject to cellsoring. It is established the strong consistency of the nearest neighbor regression estimator