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Statistical Fitting Criterion on the Basis of Cross-Validation Estimation

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Abstract

The statistical properties of cross-validation estimation as a criterion for choosing a decision model (a method for generating the decision function) are studied in the paper. For the variance analysis problem it is proved that the cross-validation criterion is equivalent to Fisher’s criterion for testing a homogeneity hypothesis under a certain significance level. It is revealed that the cross-validation criterion used for choosing the decision function among a certain one-parameter class and optimal decision function generation in the framework of a Bayesian model with normal parameter distribution are the same.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Koptyuga 4, Novosibirsk, 630090, Russia

    V. M. Nedel’ko

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  1. V. M. Nedel’ko
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Correspondence to V. M. Nedel’ko.

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Viktor Mikhailovich Nedel’ko, born in 1971, graduated from Novosibirsk State University in 1993. Candidate of mathematical and physical sciences, associate professor, Sobolev Institute of Mathematics of Siberian Branch of the Russian Academy of Sciences. Fields of interests: mathematical methods of data mining (machine learning), mathematical statistics, artificial intelligence. Publications: more than 60 papers.

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Nedel’ko, V.M. Statistical Fitting Criterion on the Basis of Cross-Validation Estimation. Pattern Recognit. Image Anal. 28, 510–515 (2018). https://doi.org/10.1134/S1054661818030148

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  • DOI: https://doi.org/10.1134/S1054661818030148

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