Bahadur representation of nonparametric M-estimators for spatial processes

Chen, Jia, Li, Degui and Zhang, Lixin (2008) Bahadur representation of nonparametric M-estimators for spatial processes. Acta Mathematica Sinica, 24 11: 1871-1882.


Author Chen, Jia
Li, Degui
Zhang, Lixin
Title Bahadur representation of nonparametric M-estimators for spatial processes
Journal name Acta Mathematica Sinica  (ERA 2012 Listed)    (ERA 2010 Rank B)   Check publisher's open access policy
Publication date 2008-11
Sub-type Article
DOI 10.1007/s10114-008-6589-2
Volume number 24
Issue number 11
ISSN 1439-8516; 1439-7617
Start page 1871
End page 1882
Total pages 12
Place of publication Heidelberg, Germany
Publisher Springer
Language eng
Formatted abstract Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the so-called optimal bandwidth hn = O(|n|-1/5), n ∈ Zd, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(|n|-4/5 log |n|). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.
Keyword Bahadur representation
Local linear M-estimator
Spatial processes
Strongly mixing
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Acta Mathematica Sinica, English Series

Document type: Journal Article
Sub-type: Article
Collection: School of Mathematics and Physics
 
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Created: Thu, 01 Sep 2011, 14:17:39 EST by Dr Jia Chen on behalf of Mathematics