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Дата последнего поиска статьи во внешних источниках: 2 сентября 2014 г.
Аннотация:The paper treats a new approach to reducing the dimension of factors which affect the non-binary response variable Y. This is relevant in analysis of a number of stochastic models, for instance, in biological and medical studies. The quality of Y estimation by means of a function in those factors is described by a specified error functional. It involves a penalty function to take into account the importance of the forecast for different response values. The joint distribution of factors and response variable is unknown. Thus it is quite natural to employ for statistical inference the estimates of the error functional constructed by prediction algorithm and cross-validation procedure. One of our main results provides the criterion of strong consistency of such estimates as the number of observations tends to infinity. Due to this result one can identify the significant factors. We introduce also the regularized versions of estimates and establish for them the central limit theorem (CLT). The statistical variant of our CLT permits to construct the approximate confidence intervals for unknown error functional.