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

TY - JOUR

T1 - Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors

AU - Chen, Jia

AU - Li, Degui

AU - Lin, Zhengyan

N1 - (C) 2011 Elsevier B.V. All rights reserved.

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

KW - Nonparametric M-estimator

KW - LOCAL M-ESTIMATOR

KW - TIME-SERIES

KW - Asymptotic expansion

KW - LINEAR-REGRESSION

KW - RANGE DEPENDENT ERRORS

KW - Long-memory linear processes

UR - http://www.scopus.com/inward/record.url?scp=79955867620&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2011.03.025

DO - 10.1016/j.jspi.2011.03.025

M3 - Article

SN - 0378-3758

VL - 141

SP - 3035

EP - 3046

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 9

ER -