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

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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.

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Authors and Affiliations

  1. University of Petroleum and Minerals, Saudi Arabia

    Ibrahim A. Ahmad

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  1. Ibrahim A. Ahmad
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Research supported by a faculty summer research grant MS-STAT-42 from the University of Petroleum and Minerals.

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Ahmad, I.A. Integrated mean square properties of density estimation by orthogonal series methods for dependent variables. Ann Inst Stat Math 34, 339–350 (1982). https://doi.org/10.1007/BF02481033

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  • DOI: https://doi.org/10.1007/BF02481033

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