摘要
设随机变量Ｘ有密度函数ｆ（ｘ），Ｘ１，…，Ｘｎ为ｆ（ｘ）的子样．本文基于Ｘ１，…，Ｘｎ定义了一类ｆ（ｘ）的估计ｆｎ（ｘ），在ｆ满足局部的Ｌｉｐｓｃｈｉｔｚ条件时，获得了ｆｎ（ｘ）的渐近正态性及Ｂｅｒｙ－Ｅｓｅｅｎ界，进而得到了ｆｎ（ｘ）的渐近置信度为α的大样本置信区间．
Let X be a random variable with density function f,X 1,…,X n be the sample of f .Based on X 1,…,X n ,we define estimates f n(x) of f and obtain the asymptotical normality and Berry Esseen bound for f n(x) ,where f satisfies local lipschitz condition,the confidence intervals of confidence level α for f n(x) are also given.
