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Limits to classification and regression estimation from ergodic processes. (English) Zbl 0933.62033
Summary: 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 estimation from ergodic processes.

MSC:
62G08 Nonparametric regression and quantile regression
62M99 Inference from stochastic processes
62G07 Density estimation
60G10 Stationary stochastic processes
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