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Regression quantiles and related processes under long range dependent errors

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Regression quantiles and related processes under long range dependent errors. / Koul, Hira L.; Mukherjee, Kanchan.
In: Journal of Multivariate Analysis, Vol. 51, No. 2, 11.1994, p. 318-337.

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Koul HL, Mukherjee K. Regression quantiles and related processes under long range dependent errors. Journal of Multivariate Analysis. 1994 Nov;51(2):318-337. doi: 10.1006/jmva.1994.1065

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Koul, Hira L. ; Mukherjee, Kanchan. / Regression quantiles and related processes under long range dependent errors. In: Journal of Multivariate Analysis. 1994 ; Vol. 51, No. 2. pp. 318-337.

Bibtex

@article{ce2771e79a3545469178fb04c5b36961,
title = "Regression quantiles and related processes under long range dependent errors",
abstract = "This paper obtains asymptotic representations of the regression quantiles and the regression rank-scores processes in linear regression setting when the errors are a function of Gaussian random variables that ale stationary and long range dependent. These representations are then used to obtain the limiting behavior of L- and linear regression rank-scores statistics based on the above processes. The paper also obtains the asymptotic uniform linearity of the linear regression rank-scores processes and statistics based on residuals under the long range dependent setup. It thus generalizes some of the results of Jure{\v c}kov{\'a} [In Proceedings of the Meeting on Nonparametric Statistics and Related topics (A. K. Md. E. Saleh, Ed.) pp. 217-228. Elsevier, Amsterdam/New York] and Gutenbrunner and Jure{\v c}kov{\'a} [Ann. Statist. 20 305-329] for the case of independent errors to one of the highly useful dependent errors setup. ",
keywords = "Hermite rank, regression rank scores processes, linearity",
author = "Koul, {Hira L.} and Kanchan Mukherjee",
year = "1994",
month = nov,
doi = "10.1006/jmva.1994.1065",
language = "English",
volume = "51",
pages = "318--337",
journal = "Journal of Multivariate Analysis",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Regression quantiles and related processes under long range dependent errors

AU - Koul, Hira L.

AU - Mukherjee, Kanchan

PY - 1994/11

Y1 - 1994/11

N2 - This paper obtains asymptotic representations of the regression quantiles and the regression rank-scores processes in linear regression setting when the errors are a function of Gaussian random variables that ale stationary and long range dependent. These representations are then used to obtain the limiting behavior of L- and linear regression rank-scores statistics based on the above processes. The paper also obtains the asymptotic uniform linearity of the linear regression rank-scores processes and statistics based on residuals under the long range dependent setup. It thus generalizes some of the results of Jurečková [In Proceedings of the Meeting on Nonparametric Statistics and Related topics (A. K. Md. E. Saleh, Ed.) pp. 217-228. Elsevier, Amsterdam/New York] and Gutenbrunner and Jurečková [Ann. Statist. 20 305-329] for the case of independent errors to one of the highly useful dependent errors setup.

AB - This paper obtains asymptotic representations of the regression quantiles and the regression rank-scores processes in linear regression setting when the errors are a function of Gaussian random variables that ale stationary and long range dependent. These representations are then used to obtain the limiting behavior of L- and linear regression rank-scores statistics based on the above processes. The paper also obtains the asymptotic uniform linearity of the linear regression rank-scores processes and statistics based on residuals under the long range dependent setup. It thus generalizes some of the results of Jurečková [In Proceedings of the Meeting on Nonparametric Statistics and Related topics (A. K. Md. E. Saleh, Ed.) pp. 217-228. Elsevier, Amsterdam/New York] and Gutenbrunner and Jurečková [Ann. Statist. 20 305-329] for the case of independent errors to one of the highly useful dependent errors setup.

KW - Hermite rank

KW - regression rank scores processes

KW - linearity

U2 - 10.1006/jmva.1994.1065

DO - 10.1006/jmva.1994.1065

M3 - Journal article

VL - 51

SP - 318

EP - 337

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -