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

Jia Chen, Degui Li*, Zhengyan Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)3035-3046
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume141
Issue number9
DOIs
Publication statusPublished - Sep 2011

Bibliographical note

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

Keywords

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

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