AANA样本下非参数回归模型的相合性  

The Consistency of Nonparametric Regression Model Under AANA Samples

作　　者：张水利 屈聪 侯甜甜 张晓飞 ZHANG Shuili;QU Cong;HOU Tiantian;ZHANG Xiaofei(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan 467000)

机构地区：[1]平顶山学院数学与统计学院,平顶山467000

出　　处：《系统科学与数学》2022年第2期473-486,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11701307);平顶山学院高层次人才科研启动基金项目(PXY-BSQD2016006)资助课题。

摘　　要：文章在误差为AANA序列的条件下,利用截尾方法及AANA序列的指数不等式,研究了非参数回归模型P-C估计量的p阶矩相合性、强相合性、完全相合性,且得到了完全相合性的收敛速度,所得结论推广和拓展了已有相关结果.最后,通过数值模拟对主要结果进行了验证.In this paper,we establish the p-th moment consistency,strong consistency and complete consistency of the P-C estimator in nonparametric regression model under AANA samples,using truncation method and exponential inequalities of A AN A,and we also obtain the rate of complete consistency.The results extend the existing related conclusions.Finally,the main results are verified by a numerical simulation.

关 键 词：AANA变量 非参数回归模型 完全相合性 矩相合性 P-C估计量 

分 类 号：O212.1[理学—概率论与数理统计]