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Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors.

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Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. / Koul, Hira L.; Mukherjee, Kanchan.
In: Probability Theory and Related Fields, Vol. 95, No. 4, 12.1993, p. 535-553.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Koul, HL & Mukherjee, K 1993, 'Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors.', Probability Theory and Related Fields, vol. 95, no. 4, pp. 535-553. https://doi.org/10.1007/BF01196733

APA

Koul, H. L., & Mukherjee, K. (1993). Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. Probability Theory and Related Fields, 95(4), 535-553. https://doi.org/10.1007/BF01196733

Vancouver

Koul HL, Mukherjee K. Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. Probability Theory and Related Fields. 1993 Dec;95(4):535-553. doi: 10.1007/BF01196733

Author

Koul, Hira L. ; Mukherjee, Kanchan. / Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. In: Probability Theory and Related Fields. 1993 ; Vol. 95, No. 4. pp. 535-553.

Bibtex

@article{636277be66614f65b70a4003cafad286,
title = "Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors.",
abstract = "This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.",
author = "Koul, {Hira L.} and Kanchan Mukherjee",
year = "1993",
month = dec,
doi = "10.1007/BF01196733",
language = "English",
volume = "95",
pages = "535--553",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "4",

}

RIS

TY - JOUR

T1 - Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors.

AU - Koul, Hira L.

AU - Mukherjee, Kanchan

PY - 1993/12

Y1 - 1993/12

N2 - This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.

AB - This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.

U2 - 10.1007/BF01196733

DO - 10.1007/BF01196733

M3 - Journal article

VL - 95

SP - 535

EP - 553

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -