Kernel density estimation for linear processes

Abstract

Let X1,...,Xn be n consecutive observations of a linear process , where [mu] is a constant and {Zt} is an innovation process consisting of independent and identically distributed random variables with mean zero and finite variance. Assume that X1 has a probability density [latin small letter f with hook]. Uniform strong consistency of kernel density estimators of [latin small letter f with hook] is established, and their rates of convergence are obtained. The estimators can achieve the rate of convergence (n-1 log n)1/3 in L[infinity] norm restricted to compacts under weak conditions.kernel density estimator bandwidth linear process uniform convergence