The Annals of Statistics

Limits to classification and regression estimation from ergodic processes

Andrew B. Nobel

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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.

Article information

Source
Ann. Statist., Volume 27, Number 1 (1999), 262-273.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1018031110

Digital Object Identifier
doi:10.1214/aos/1018031110

Mathematical Reviews number (MathSciNet)
MR1701110

Zentralblatt MATH identifier
0933.62033

Subjects
Primary: 62G07: Density estimation
Secondary: 60G10: Stationary processes 62M99: None of the above, but in this section

Keywords
Classification regression ergodic processes counterexamples reduction arguments

Citation

Nobel, Andrew B. Limits to classification and regression estimation from ergodic processes. Ann. Statist. 27 (1999), no. 1, 262--273. doi:10.1214/aos/1018031110. https://projecteuclid.org/euclid.aos/1018031110


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