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Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors

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Publication details

JournalJournal of Statistical Planning and Inference
DatePublished - Sep 2011
Issue number9
Number of pages12
Pages (from-to)3035-3046
Original languageEnglish


We consider asymptotic expansion of the nonparametric M-estimator in a fixed-design nonlinear regression model when the errors are generated by long-memory linear processes. Under mild conditions, we show that the nonparametric M-estimator is first-order equivalent to the Nadaraya-Watson (NW) estimator, which implies that the nonparametric M-estimator has the same asymptotic distribution as that of the NW estimator. Furthermore, we study the second-order asymptotic expansion of the nonparametric M-estimator and show that the difference between the nonparametric M-estimator and the NW estimator has a limiting distribution after suitable standardization. The nature of the limiting distribution depends on the range of long-memory parameter alpha. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.

Bibliographical note

(C) 2011 Elsevier B.V. All rights reserved.

    Research areas

  • Nonparametric M-estimator, LOCAL M-ESTIMATOR, TIME-SERIES, Asymptotic expansion, LINEAR-REGRESSION, RANGE DEPENDENT ERRORS, Long-memory linear processes

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