Аннотация:
Within the penalized model selection approach the selected model is defined by minimization of penalized empirical risk. Such procedures enjoy nice algorithmic properties especially if both the empirical risk and the penalty function are convex functions of the parameter. A number of “oracle” risk bounds for such methods are available. However, the choice of penalty is critical and there is no unified approach for fixing this penalty. This talk presents another method of model selection based on a smallest accepted rule: a model is accepted if it is not rejected against any larger model . The final choice is the simplest accepted model. Model comparison is being done by multiple testing with critical values tuned by a bootstrap procedure. We present some oracle results on subset and parameter estimation for the proposed method.
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