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