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Universally consistent conditionalU-statistics for absolutely regular processes and its applications for hidden Markov models

  • Estimation
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Abstract

A general class of conditionalU-statistics was introduced by W. Stute as a generalization of the Nadaraya-Watson estimates of a regression function. It was shown that such statistics are universally consistent. Also, universal consistentcies of the window andk n -nearest neighbor estimators (as two special cases of the conditionalU-statistics) were proved. In this paper, we extend these results from the independent case to dependent case. The result is applied to verify the Bayes risk consistency of the corresponding discrimination rules.

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Author information

Authors and Affiliations

  1. UMRC 55830 C.N.R.S. and IUFM du Limousin, 209 Bd de Vanteaux, F87036, Limoges Cedex, France

    Michel Harel

  2. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Madan L. Puri

Authors
  1. Michel Harel
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  2. Madan L. Puri
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Additional information

Research supported by the Office of Naval Research Contract N00014-91-J-1020.

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Harel, M., Puri, M.L. Universally consistent conditionalU-statistics for absolutely regular processes and its applications for hidden Markov models. Ann Inst Stat Math 56, 819–832 (2004). https://doi.org/10.1007/BF02506491

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  • DOI: https://doi.org/10.1007/BF02506491

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