Limits to Classification and Regression Estimation from Ergodic Processes

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...

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Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 27(1999), 1, Seite 262-273
1. Verfasser: Nobel, Andrew B. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1999
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... Behavioral sciences Information science
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520 |a 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. 
540 |a Copyright 1999 The Institute of Mathematical Statistics 
650 4 |a Primary 62G07 
650 4 |a Secondary 60G10, 62M99 
650 4 |a Classification 
650 4 |a Regression 
650 4 |a Ergodic processes 
650 4 |a Counterexamples 
650 4 |a Reduction arguments 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables  |x Stochastic processes  |x Ergodic processes 
650 4 |a Physical sciences  |x Physics  |x Mechanics  |x Density  |x Density measurement  |x Density estimation 
650 4 |a Applied sciences  |x Systems science  |x Systems theory  |x Dynamical systems  |x Ergodic theory 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Decision making 
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650 4 |a Information science  |x Data products  |x Datasets  |x Time series 
650 4 |a Applied sciences  |x Computer science  |x Artificial intelligence  |x Machine learning  |x Perceptron convergence procedure 
650 4 |a Mathematics  |x Mathematical analysis  |x Measure theory  |x Lebesgue measures 
650 4 |a Mathematics 
650 4 |a Information science  |x Information analysis  |x Data analysis  |x Time series analysis  |x Time series forecasting  |x Time Series and Stochastic Regression 
655 4 |a research-article 
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