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Central Limit Theorem Related to MDR-Method

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Asymptotic Laws and Methods in Stochastics

Part of the book series: Fields Institute Communications ((FIC,volume 76))

Abstract

In many medical and biological investigations, including genetics, it is typical to handle high dimensional data which can be viewed as a set of values of some factors and a binary response variable. For instance, the response variable can describe the state of a patient health and one often assumes that it depends only on some part of factors. An important problem is to determine collections of significant factors. In this regard we turn to the MDR-method introduced by M. Ritchie and coauthors. Our recent paper provided the necessary and sufficient conditions for strong consistency of estimates of the prediction error employing the K-fold cross-validation and an arbitrary penalty function. Here we introduce the regularized versions of the mentioned estimates and prove for them the multidimensional CLT. Statistical variants of the CLT involving self-normalization are discussed as well.

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Acknowledgements

The author is grateful to Organizing Committee for invitation to participate in the Fields Institute International Symposium on Asymptotic Methods in Stochastics, in Honour of Miklós Csörgő’s Work. Special thanks are due to Professor Csörgő and his colleagues for hospitality.

The work is partially supported by RFBR grant 13-01-00612.

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Correspondence to Alexander Bulinski .

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Bulinski, A. (2015). Central Limit Theorem Related to MDR-Method. In: Dawson, D., Kulik, R., Ould Haye, M., Szyszkowicz, B., Zhao, Y. (eds) Asymptotic Laws and Methods in Stochastics. Fields Institute Communications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3076-0_7

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