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February 1999 Limits to classification and regression estimation from ergodic processes
Andrew B. Nobel
Ann. Statist. 27(1): 262-273 (February 1999). DOI: 10.1214/aos/1018031110

Abstract

We answer two open questions concerning the existence of universal schemes for classification and regression estimation from stationary ergodic processes. It is shown that no measurable procedure can produce weakly consistent regression estimates from every bivariate stationary ergodic process, even if the covariate and response variables are restricted to take values in the unit interval. It is further shown that no measurable procedure can produce weakly consistent classification rules from every bivariate stationary ergodic process for which the response variable is binary valued. The results of the paper are derived via reduction arguments and are based in part on recent work concerning density estimaton from ergodic processes.

Citation

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Andrew B. Nobel. "Limits to classification and regression estimation from ergodic processes." Ann. Statist. 27 (1) 262 - 273, February 1999. https://doi.org/10.1214/aos/1018031110

Information

Published: February 1999
First available in Project Euclid: 5 April 2002

MathSciNet: MR1701110
zbMATH: 0933.62033
Digital Object Identifier: 10.1214/aos/1018031110

Subjects:
Primary: 62G07
Secondary: 60G10, 62M99

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 1 • February 1999
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