Convergence of Hermite Series Density Estimators Under Conditions of Weak Dependence

摘要

In this paper we study convergence properties of Hermite series estimators for stationary mixing sequences. We assume that the sample is a part of a stationary sequence fulfilling theα-mixing, theϕ-mixing condition or the condition of absolute regularity. We derive convergence results for the mean square error (MSE) and the mean integrated square error (MISE) as well as results concerning uniform strong convergence. Under suitable assumptions, particularly for mixing sequences with a fast decay of the mixing coefficients, we get the same asymptotic properties as known from the i.i.d. sample case.