Preprint #98-13

  Adaptive Estimation in Pattern Recognition by Combining Different Procedures   by   Yuhong Yang Department of Statistics Iowa State University   Abstract   We study a problem of adaptive estimation of a conditional probability function in a pattern recognition setting. In many applications, for more flexibility, one may want to consider various estimation procedures targeted at different scenarios and/or under different assumptions. For example, when the feature dimension is high, to overcome the familiar curse of dimensionality, one may seek a good parsimonious model among a number of candidates such as CART, neural nets, additive models, and others. For such a situation, one wishes to have an automated final procedure performing always as well as the best candidate.
 
In this work, we propose a method to combine a countable collection of procedures for estimating the conditional probability. We show that the combined procedure has a property that its statistical risk is bounded above by that of any of the procedure being considered plus a small penalty. Thus in an asymptotic sense, the strengths of the different estimation procedures in accuracy are shared by the combined procedure.
 
Keywords and phrases: Adaptive estimation; conditional probability; minimax-rate adaptation, nonparametric classification.
 
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