摘要
设（Ｘｉ，Ｙｉ），ｉ＝１，…，ｎ是从取值于ＲｄＸＲ１的随机向量（Ｘ，Ｙ）中抽取的ｉｄ样本，Ｅ（｜Ｙ｜）＜∞，而以ｍ（ｘ）＝Ｅ（Ｙ｜Ｘ＝ｘ）表示回归函数．在合适条件下获得了一类基于完全和截尾数据回归函数核估计的逐点相合性，所获的结果对于所有Ｘ的分布μ均成立。
Let (X,Y ) be a R d×R 1 Valued random vector with E(| Y |)<∞, m(x) =E( Y|X=x ) be the regression function of Y with respect to X . Suppose that ( X i,Y i),i=1,…,n are iid samples drawn from (X,Y) .It is desired to estimate m(x) based on these samples. Based on complete and censored data, we obtain pointwise consistency of regression function kernel estimates under suitable conditions, the results are distribution-free in the sense that they are true for all distributions μ of X .
出处
《郑州工业大学学报》
1999年第1期60-63,共4页
Journal of Zhengzhou University of Technology
关键词
回归函数
核估计
分布自由
相合性
非参数统计
censored data
regression function
kernel estimate
distribution free
