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

Jia Chen, Degui Li, Zhengyan Lin

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5 Citations (Scopus)

Abstract

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 Nadarayaa??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 I?. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.
Original languageEnglish
Pages (from-to)3035 - 3046
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume141
Issue number9
DOIs
Publication statusPublished - 2011
Externally publishedYes

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