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

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.