Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

TY - JOUR

T1 - Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

AU - Chen, Jia

AU - Li, Degui

AU - Zhang, Li Xin

PY - 2008/11/1

Y1 - 2008/11/1

N2 - 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 h(n) = O(vertical bar n vertical bar(-1/5)), n epsilon Z(d), 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(vertical bar n vertical bar(-4/5) log vertical bar n vertical bar). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.

AB - 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 h(n) = O(vertical bar n vertical bar(-1/5)), n epsilon Z(d), 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(vertical bar n vertical bar(-4/5) log vertical bar n vertical bar). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.

KW - strongly mixing

KW - Bahadur representation

KW - RANDOM-FIELDS

KW - LOCAL M-ESTIMATOR

KW - TIME-SERIES

KW - MODELS

KW - local linear M-estimator

KW - REGRESSION

KW - spatial processes

KW - DENSITY-ESTIMATION

UR - http://www.scopus.com/inward/record.url?scp=55149085310&partnerID=8YFLogxK

U2 - 10.1007/s10114-008-6589-2

DO - 10.1007/s10114-008-6589-2

M3 - Article

SN - 1439-8516

VL - 24

SP - 1871

EP - 1882

JO - Acta mathematica sinica-English series

JF - Acta mathematica sinica-English series

IS - 11

ER -