Limits to Classification and Regression Estimation from Ergodic Processes
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...
| Veröffentlicht in: | The Annals of Statistics. - Institute of Mathematical Statistics. - 27(1999), 1, Seite 262-273 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1999
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| Zugriff auf das übergeordnete Werk: | The Annals of Statistics |
| Schlagworte: | Primary 62G07 Secondary 60G10, 62M99 Classification Regression Ergodic processes Counterexamples Reduction arguments Mathematics Physical sciences Applied sciences mehr... |
| Zusammenfassung: | 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. |
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| ISSN: | 00905364 |