Regression quantiles and related processes under long range dependent errors

Koul, Hira L. and Mukherjee, Kanchan (1994) Regression quantiles and related processes under long range dependent errors. Journal of Multivariate Analysis, 51 (2). pp. 318-337.

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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.

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Journal Article
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Journal of Multivariate Analysis
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15 Jul 2013 09:10
Last Modified:
27 Apr 2022 02:07