回归函数改良核估计的渐近分布
Asymptotic Distribution of the Improved Kernel Regression Function Estimates
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摘要: 设（X1,Y1）,…,（Xn,Yn）是来自二元总体（X,Y）的样本，若EY＜∞，则回归函数m（x）=E（Y|X=x）存在．在本文中，考虑m（x）的改良核估计:\widehatm_n(x)=\sum_i=1^n Y_i I（Yi＜bn）K(\fracx-X_ih_n)/\sum_i=1^n Y_i IK(\fracx-X_ih_n) 其中K是一元概率密度,0＜ hn → 0,0 ＜bn → ∞（n→∞）我们分别在i.i.d.和平稳ϕ-mixing相依情况下，得出了^mn(x)的渐近分布。Abstract: Suppose that （X1, Y1）,…, （Xn, Yn） is a random sample sequence from （X, Y）, If EY is finite, the regression function m （of Y on X） is defined by m（x）= E（Y|X = x）. In this paper, we obtain the asymptotic normality of the improved kernel regression function estimates \widehatm_n(x)=\sum_i=1^n Y_i I（Yi＜bn）K(\fracx-X_ih_n)/\sum_i=1^n Y_i IK(\fracx-X_ih_n) . Where K is a univariate density function, 0 ＜ hn → 0 and 0 ＜bn → ∞ （n → ∞）.
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