Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 3, Pages 233-254
doi:10.1155/S1048953396000238

Nonparametric density estimators based on nonstationary absolutely regular random sequences

Michel Harel1,2 and Madan L. Puri1,2

1I.U.F.M. du Limousin, U.R.A. 745 C.N.R.S., Toulouse, France
2Indiana University , Dept. of Mathematics, USA

Received 1 May 1995; Revised 1 November 1995

Copyright © 1996 Michel Harel and Madan L. Puri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.