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On Foundation of the Dimensionality Reduction Method for Explanatory Variables

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Study of many complex phenomena involves data sets of high dimension. This is typical for many medical and biological studies, especially in genetics and pharmacology. We treat binary response variable (showing, e.g., the state of patient’s health) depending on n discrete factors (explanatory variables). To find the most significant among them is a very important problem. The aim of the paper is to establish necessary and sufficient conditions for the strong consistency of the specified estimates employing the cross-validation of the error arising in prediction algorithm for the response variable. The impact of the choice of a function is discussed as well. The obtained results provide a basis for the well-known MDR-method widely used in genetic data analysis.

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  1. Moscow State University, Moscow, Russia

    A. V. Bulinski

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  1. A. V. Bulinski
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Correspondence to A. V. Bulinski.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 408, 2012, pp. 84–101.

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Bulinski, A.V. On Foundation of the Dimensionality Reduction Method for Explanatory Variables. J Math Sci 199, 113–122 (2014). https://doi.org/10.1007/s10958-014-1838-7

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  • DOI: https://doi.org/10.1007/s10958-014-1838-7

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