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  (ERA 2012 Listed)    (ERA 2010 Rank A)   Check publisher's open access policy
Publication date 2011-09
Sub-type Article
DOI 10.1016/j.jspi.2011.03.025
Volume number 141
Issue number 9
ISSN 0378-3758; 1873-1171
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
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