φ-混合下回归函数改良核估计的渐近正态性

Asymptotic Normality of the Improved Kernel Estimator for Regression Function under φ -mixing Samples

设{(Xi,Yi),i≥1}是从取值于Rd×R的总体(X,Y)中抽取的严平稳、φ-混合样本.回归函数m(x)=E(Y|X=x)改良的递归核估计定义为本文在适当的条件下,讨论了mn(2)(x)的渐近正态性.

Let {（Xi,Yi）,i ≥ 1} be a strictly stationary and φ-mixing sample sequence from （X, Y） in R^d × R. The improved recursive kernel estimator of regression function m（x） = E（Y│X = x） isdefined by m^⌒（n）^（2）=[∑（i=1）^nYiI（│Yi│＜bi）h（i）^-dK（--（hi）^x-Xi）]/[∑（j=1）^nh（j）^-dk（--（hj）^x-Xj）]. Under suitable conditions, we prove the asymptotic normality of m^⌒（n）^（2）.