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March, 1987 Robust Spectral Regression
Alexander M. Samarov
Ann. Statist. 15(1): 99-111 (March, 1987). DOI: 10.1214/aos/1176350255

Abstract

This paper addresses the problem of linear regression estimation when the disturbances follow a stationary process with its spectral density known only to be in a neighborhood of some specified spectral density, for instance, that of white noise. Rather than trying to adapt to a small unspecified autocorrelation, we follow here the robustness approach, and establish the extent of the regressors and disturbance spectra interaction which require serial correlation correction. We consider a class of generalized least-squares estimates, and find the estimator in this class which optimally robustifies the least-squares estimator against serial correlation. The estimator, when considered in the frequency domain, is of a form of weighted least squares with the most prominent frequencies of the regression spectrum being downweighted in a way similar to Huber's robust regression estimator.

Citation

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Alexander M. Samarov. "Robust Spectral Regression." Ann. Statist. 15 (1) 99 - 111, March, 1987. https://doi.org/10.1214/aos/1176350255

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0644.62095
MathSciNet: MR885726
Digital Object Identifier: 10.1214/aos/1176350255

Subjects:
Primary: 62J02
Secondary: 62F35 , 62M10 , 62M15

Keywords: efficiency robustness , generalized least squares , minimax robustness , regression spectrum , serial correlation

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 1 • March, 1987
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