相依样本下非参数回归函数估计的强收敛速度

Strong Consistence Rate of Estimator of a Nonparametric Regression Function under Dependent Samples

设(X,Y),(X_1,Y_1,),…,(X_n,Y_n)是一个平稳、φ—混合过程((X,Y)∈R^d×R,E|Y|^(s+δ)<∞,s≥2,δ>0),用m(x)记E{Y|X=x},本文讨论了m(x)的如下估计m_n(x)的强收敛速度:

Suppose that(X,Y),(X_1,Y_1),…,(X_n,Y_n) is a stationary and φ-mixing process((X,Y)∈R^d×R, E\Y\^(s+δ)<∞, s≥2, δ>0). Let m(x) denote E{Y\X=x}. This paper discusses the strong convergence rate of the estimator m_n(x) of m(x), wherem_n(x) =sum from i=1 to n h_i(-d)Y_iK((X_i-x)/h_i)/sum from j=1 to m h_j^(-d)K((X_j-x)/h_j).