Abstract
For nonbinary response variable depending on a finite collection of factors with values in a finite subset of R the problem of the optimal forecast is considered. The quality of prediction is described by the error function involving a penalty function. The criterion of almost sure convergence to unknown error function for proposed estimates constructed by means of a prediction algorithm and K -fold cross-validation procedure is established. It is demonstrated that imposed conditions admit the efficient verification. The developed approach permits to realize the dimensionality reduction of factors under consideration. One can see that the results obtained provide the base to identify the set of significant factors. Such problem arises, e.g., in medicine and biology. The central limit theorem for proposed statistics is proven as well. In this way one can indicate the approximate confidence intervals for employed error function.
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