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

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https://link.springer.com/chapter/10.1007%2F978-3-7908-2628-9_2

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2010-09

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Physica-Verlag HD

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https://hdl.handle.net/2022/22053

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 kn-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.

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Elharfaoui E., Harel M., Puri M.L. (2011) Asymptotic Behavior of the Universally Consistent Conditional U-Statistics for Nonstationary and Absolutely Regular Processes. In: Wells M., SenGupta A. (eds) Advances in Directional and Linear Statistics. Physica-Verlag HD

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https://doi.org/10.1007/978-3-7908-2628-9_2

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Madan Lal Puri Collection