Asymptotic Behavior of the Universally Consistent Conditional U-Statistics for Nonstationary and Absolutely Regular Processes

Echarif Elharfaoui (), Michel Harel and Madan L. Puri
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Echarif Elharfaoui: Université Chouaîb Doukkali, Département de Mathématiques et Informatique, Faculté des Sciences El Jadida

Chapter Chapter 2 in Advances in Directional and Linear Statistics, 2011, pp 11-25 from Springer

Abstract: Abstract A general class of conditional U-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 consistencies of the window and k n -nearest neighbor estimators (as two special cases of the conditional U-statistics) were proved. Later, (Harel and Puri, Ann Inst Stat Math 56(4):819–832, 2004) extended his results from the i.i.d. case to the absolute regular case. In this paper, we extend these results from the stationary case to the nonstationary case.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2628-9_2

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DOI: 10.1007/978-3-7908-2628-9_2

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