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Independent rule in classification of multivariate binary data

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  • Park, Junyong

Abstract

We consider the performance of the independent rule in classification of multivariate binary data. In this article, broad studies are presented including the performance of the independent rule when the number of variables, d, is fixed or increased with the sample size, n. The latter situation includes the case of d=O(n[tau]) for [tau]>0 which cover "the small sample and the large dimension", namely d>>n when [tau]>1. Park and Ghosh [J. Park, J.K. Ghosh, Persistence of plug-in rule in classification of high dimensional binary data, Journal of Statistical Planning and Inference 137 (2007) 3687-3707] studied the independent rule in terms of the consistency of misclassification error rate which is called persistence under growing numbers of dimensions, but they did not investigate the convergence rate. We present asymptotic results in view of the convergence rate under some structured parameter space and highlight that variable selection is necessary to improve the performance of the independent rule. We also extend the applications of the independent rule to the case of correlated binary data such as the Bahadur representation and the logit model. It is emphasized that variable selection is also needed in correlated binary data for the improvement of the performance of the independent rule.

Suggested Citation

  • Park, Junyong, 2009. "Independent rule in classification of multivariate binary data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2270-2286, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2270-2286
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    References listed on IDEAS

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    1. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    2. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    3. J. D. Wilbur & J. K. Ghosh & C. H. Nakatsu & S. M. Brouder & R. W. Doerge, 2002. "Variable Selection in High-Dimensional Multivariate Binary Data with Application to the Analysis of Microbial Community DNA Fingerprints," Biometrics, The International Biometric Society, vol. 58(2), pages 378-386, June.
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    Cited by:

    1. Park, Junyong & Park, DoHwan, 2015. "Stein’s method in high dimensional classification and applications," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 110-125.
    2. Bulinski, Alexander & Rakitko, Alexander, 2015. "MDR method for nonbinary response variable," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 25-42.
    3. Junyong Park, 2019. "Testing homogeneity of proportions from sparse binomial data with a large number of groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 505-535, June.

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