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

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Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors. / Chen, Jia; Li, Degui; Lin, Zhengyan.

In: Journal of Statistical Planning and Inference, Vol. 141, No. 9, 09.2011, p. 3035-3046.

Research output: Contribution to journal › Article

Harvard

Chen, J, Li, D & Lin, Z 2011, 'Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors', Journal of Statistical Planning and Inference, vol. 141, no. 9, pp. 3035-3046. https://doi.org/10.1016/j.jspi.2011.03.025

APA

Chen, J., Li, D., & Lin, Z. (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. https://doi.org/10.1016/j.jspi.2011.03.025

Vancouver

Chen J, Li D, Lin Z. Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors. Journal of Statistical Planning and Inference. 2011 Sep;141(9):3035-3046. https://doi.org/10.1016/j.jspi.2011.03.025

Author

Chen, Jia ; Li, Degui ; Lin, Zhengyan. / Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors. In: Journal of Statistical Planning and Inference. 2011 ; Vol. 141, No. 9. pp. 3035-3046.

Bibtex - Download

@article{607ab9047fe84629b228178e39badddc,
title = "Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors",
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 alpha. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.",
keywords = "Nonparametric M-estimator, LOCAL M-ESTIMATOR, TIME-SERIES, Asymptotic expansion, LINEAR-REGRESSION, RANGE DEPENDENT ERRORS, Long-memory linear processes",
author = "Jia Chen and Degui Li and Zhengyan Lin",
note = "(C) 2011 Elsevier B.V. All rights reserved.",
year = "2011",
month = sep,
doi = "10.1016/j.jspi.2011.03.025",
language = "English",
volume = "141",
pages = "3035--3046",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "9",

}

RIS (suitable for import to EndNote) - Download

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

VL - 141

SP - 3035

EP - 3046

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 9

ER -

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