相依样本分布函数和回归函数核估计的强收敛性及其速度

UNIFORM STRONG CONVERGENCE AND RATES FOR THE KERNEL ESTIMATORS OF A DISTRIBUTION FUNCTION AN D A REGRESSION FUNCTION UNDER WEAKLY DEPENDENT ASSUMPTIONS

本文讨论样本为φ-混合和α-混合时分布函数核估计的强相合性.在α-混合时讨论其收敛速度,我们的结果与i.i.d.情况相一致,从而改进了[2]中的结论。同时,本文还在ρ-混合下,讨论回归函数核估计的强收敛性及收敛速度,其结果接近于独立情形。

Let X_1, X_2, …be a sequence of random variables with unknown distribution function F(x). A kernel estimator of F(x) was suggested by Yamato. Ohai (1988) considered the strong consistency and rates for the estimator under φ-mixing condition. In the paper, we study the uniform strong convergency of the estimator under φ-mixing and a-mixing assumptions and the rate of the uniform strong convergence for the estimator under α-mixing assumption. Our conditions are weaker than those of Ohai (1988) and some results are as same as i. i. d, case. Again, lot (X_1, Y_1), (X_2, Y_2), … be a sequence of p-mixing random variables. We discuss the strong consistency and rates for recursivo kernel estimator of rogression function.