摘要
设（Ｘｉ，Ｙｉ），ｉ＝１，…，ｎ是从取值于Ｒｄ × Ｒ１的随机向量（Ｘ，Ｙ）中抽取的ｉ．ｉ．ｄ．样本；Ｅ（Ｙ）＜∞，而以ｍ（ｘ）＝Ｅ（ＹＸ＝ｘ）表示回归函数．在截尾情况下，观察到的不是诸Ｙｉ本身，而是Ｚｉ＝ ｍｉｎ（Ｙｉ， Ｔｉ）及 δｉ＝Ｉ（Ｙｉ≤Ｔｉ），其中Ｔｉ是与（Ｘｉ，Ｙｉ）独立的随机变量， ｉ＝ １， ２，…，ｎ．当 Ｔ的分布未知时，在一定条件下，得到了回归函数改良估计的强合性．
Let (X, Y) be a Rd × R1-Valued random vector with E(Y) < ∞ and m(x) = E(YX = x) be the regression of Y with respect to X. Suppose that (Xi, Yi), i = 1,''', n are i.i.d. samples drawn from (X, Y), it is desired to estimate m(x) based on these samples. In this paper we discuss the case that {Yi} are censored by random variables {Ti}. It means that we can only observe Zi = min(Yi,Ti) and δi = I(Yi ≤Ti). We always suppose that Ti i.i.d. and independent of (Xi, Yi). We obtain strong cosistency of regression function.
出处
《应用概率统计》
CSCD
北大核心
2000年第4期379-390,共12页
Chinese Journal of Applied Probability and Statistics
基金
国家自然科学基金
北京市自然科学基金资助项目(22304100113016
1992005).
