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...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.展开更多
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)
文摘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.
