Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

Zhengyan Lin; Degui Li; Jia Chen

doi:10.1007/s00184-006-0111-6

Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

Zhengyan Lin, Degui Li^*, Jia Chen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.

Original language	English
Pages (from-to)	289-303
Number of pages	15
Journal	Metrika
Volume	66
Issue number	3
DOIs	https://doi.org/10.1007/s00184-006-0111-6
Publication status	Published - Nov 2007

Keywords

long-range dependence
CONVERGENCE
S-estimator
consistency
linear model
asymptotic distribution
REGRESSION MODEL

Access to Document

10.1007/s00184-006-0111-6

http://link.springer.com/article/10.1007%2Fs00184-006-0111-6

Cite this

@article{aef5cc78a2f14850b2d95066365faf84,

title = "Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors",

abstract = "The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.",

keywords = "long-range dependence, CONVERGENCE, S-estimator, consistency, linear model, asymptotic distribution, REGRESSION MODEL",

author = "Zhengyan Lin and Degui Li and Jia Chen",

year = "2007",

month = nov,

doi = "10.1007/s00184-006-0111-6",

language = "English",

volume = "66",

pages = "289--303",

journal = "Metrika",

issn = "0026-1335",

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T1 - Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

AU - Lin, Zhengyan

AU - Li, Degui

AU - Chen, Jia

PY - 2007/11

Y1 - 2007/11

N2 - The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.

AB - The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.

KW - long-range dependence

KW - CONVERGENCE

KW - S-estimator

KW - consistency

KW - linear model

KW - asymptotic distribution

KW - REGRESSION MODEL

U2 - 10.1007/s00184-006-0111-6

DO - 10.1007/s00184-006-0111-6

M3 - Article

SN - 0026-1335

VL - 66

SP - 289

EP - 303

JO - Metrika

JF - Metrika

IS - 3

ER -