The Annals of Statistics

Robust Spectral Regression

Alexander M. Samarov

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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.

Article information

Ann. Statist., Volume 15, Number 1 (1987), 99-111.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62J02: General nonlinear regression
Secondary: 62F35: Robustness and adaptive procedures 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M15: Spectral analysis

Serial correlation regression spectrum efficiency robustness minimax robustness generalized least squares


Samarov, Alexander M. Robust Spectral Regression. Ann. Statist. 15 (1987), no. 1, 99--111. doi:10.1214/aos/1176350255.

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