ρ混合序列权函数估计的渐近性质

Asymptotic properties of the weighted function estimator for ρ-mixing sequence

为研究非参数回归模型中ρ混合序列权函数估计的渐近性质问题,在矩条件较合理的情形下,采用相依序列概率不等式以及截断的方法,获得了回归函数g(·)权函数估计的几乎处处收敛的强相合性;在矩条件和权函数条件较合理的情形下,利用相依序列概率不等式以及Bernstein大小分块和Lyapunov中心极限定理的方法,获得了回归函数g(·)权函数估计的渐近正态性.将其他相依序列下相应方法和结论推广到ρ混合序列.

This paper studied the asymptotic properties of the weighted function estimator for ρ-mixing sequence in the nonparametric regression model, and showed the strong consistency by probability inequalities of dependent sequences and truncation method under reasonable moment condition for the weighted function estimator of regression function g（·）. The asymptotic normality was demonstrated by probability inequalities of dependent sequences and block size method under reasonable moment and weighted function condition for the weighted function estimator of regression function g（·）, which generalize the corresponding methods and results of other dependent sequences for ρ-mixing sequence.