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MDR method for nonbinary response variable

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  • Bulinski, Alexander
  • Rakitko, Alexander

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.

Suggested Citation

  • Bulinski, Alexander & Rakitko, Alexander, 2015. "MDR method for nonbinary response variable," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 25-42.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:25-42
    DOI: 10.1016/j.jmva.2014.11.008
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    References listed on IDEAS

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    1. Park, Junyong, 2009. "Independent rule in classification of multivariate binary data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2270-2286, November.
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    Cited by:

    1. Alexander Bulinski, 2024. "Forward Selection of Relevant Factors by Means of MDR-EFE Method," Mathematics, MDPI, vol. 12(6), pages 1-25, March.

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