Annals of the Institute of Statistical Mathematics

, Volume 34, Issue 1, pp 339–350

# Integrated mean square properties of density estimation by orthogonal series methods for dependent variables

Article

## Summary

The rates at which integrated mean square and mean squre errors of nonparametric density estimation by orthogonal series method for sequences of strictly stationary strong mixing random variables are obtained. These rates are better than those known to hold for the independent case and they are shown to hold for Markov processes. In fact our results when specialized to the independent case are improvements over previously known results of Schwartz (1967,Ann. Math. Statist.,38, 1262–1265). An extension of the results to estimation of the bivariate density is also given.

## AMS 1970 subject classification

Primary G2G05 Secondary 60C10

## Key words and phrases

Density estimation strong mixing mean square rates of convergence strictly stationary sequences

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