Some Limits and Positive Results on Estimation from Ergodic Data
Dr Andrew Nobel, Department of Statistics, University of North Carolina

Abstract: The first part of the talk will address several questions concerning the existence of universal schemes for non-parametric estimation from ergodic processes. It will be shown that no procedure can produce consistent density estimates from every stationary ergodic process. Negative results for classification and regression will also be presented. The second part of the talk will be devoted to interpolation from ergodic samples. In this problem, one wishes to estimate an unknown bounded function f from pairs (X_i,f(X_i)), where the sampling points X_1, X_2,... are stationary and ergodic. The consistency of a simple finitary estimation scheme will be established. The scheme will then be applied to the problem of estimating a stationary ergodic transformation from one of its trajectories.

This seminar was held at the Department of Computer Science, Royal Holloway, University of London on 22 June 1998.

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