Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 3, Pages 233-254
Nonparametric density estimators based on nonstationary
absolutely regular random sequences
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.
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.