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A mutual information estimator with exponentially decaying bias

Author

Listed:
  • Zhang Zhiyi

    (Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA)

  • Zheng Lukun

    (Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA)

Abstract

A nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

Suggested Citation

  • Zhang Zhiyi & Zheng Lukun, 2015. "A mutual information estimator with exponentially decaying bias," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(3), pages 243-252, June.
    • Handle: RePEc:bpj:sagmbi:v:14:y:2015:i:3:p:243-252:n:2
    DOI: 10.1515/sagmb-2014-0047
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