Consistency of kernel density estimators for causal processes  

作　　者：LIN ZhengYan ZHAO YueXu 

机构地区：[1]Department of Mathematics,Zhejiang University

出　　处：《Science China Mathematics》2014年第5期1083-1108,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171303 and 61273093);the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)

摘　　要：Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are derived.Secondly,the corresponding strong convergence rates are investigated.It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d.density models are also optimal for these processes.Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated. First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean（and the true density function） are derived. Secondly,the corresponding strong convergence rates are investigated. It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d. density models are also optimal for these processes.

关 键 词：kernel density estimator consistency rate dependent measure causal process 

分 类 号：O211.5[理学—概率论与数理统计]