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

  • Michel Harel
  • Madan L. Puri
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.

Key words and phrases

Universally consistent conditionalU-statistics absolute regularity Bayes risk Hidden Markov Models 
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Copyright information

© The Institute of Statistical Mathematic 2004

Authors and Affiliations

  • Michel Harel
    • 1
  • Madan L. Puri
    • 2
  1. 1.UMRC 55830 C.N.R.S. and IUFM du LimousinLimoges CedexFrance
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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