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

Chen, Jia, Li, Degui and Lin, Zhengyan (2011) Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors. Journal of Statistical Planning and Inference, 141 9: 3035-3046.


Author Chen, Jia
Li, Degui
Lin, Zhengyan
Title Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors
Journal name Journal of Statistical Planning and Inference   Check publisher's open access policy
ISSN 0378-3758
1873-1171
Publication date 2011-09
Sub-type Article (original research)
DOI 10.1016/j.jspi.2011.03.025
Volume 141
Issue 9
Start page 3035
End page 3046
Total pages 12
Place of publication Amsterdam, Netherlands
Publisher Elsevier BV
Collection year 2012
Language eng
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 α. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.
Keyword Asymptotic expansion
Long-memory linear processes
Nonparametric M-estimator
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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Created: Thu, 01 Sep 2011, 13:18:11 EST by Dr Jia Chen on behalf of Mathematics