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Entropy based constrained inference for some HDLSS genomic models: UI tests in a Chen-Stein perspective

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  • Tsai, Ming-Tien
  • Sen, Pranab Kumar

Abstract

For qualitative data models, Gini-Simpson index and Shannon entropy are commonly used for statistical analysis. In the context of high-dimensional low-sample size (HDLSS) categorical models, abundant in genomics and bioinformatics, the Gini-Simpson index, as extended to Hamming distance in a pseudo-marginal setup, facilitates drawing suitable statistical conclusions. Under Lorenz ordering it is shown that Shannon entropy and its multivariate analogues proposed here appear to be more informative than the Gini-Simpson index. The nested subset monotonicity prospect along with subgroup decomposability of some proposed measures are exploited. The usual jackknifing (or bootstrapping) methods may not work out well for HDLSS constrained models. Hence, we consider a permutation method incorporating the union-intersection (UI) principle and Chen-Stein Theorem to formulate suitable statistical hypothesis testing procedures for gene classification. Some applications are included as illustration.

Suggested Citation

  • Tsai, Ming-Tien & Sen, Pranab Kumar, 2010. "Entropy based constrained inference for some HDLSS genomic models: UI tests in a Chen-Stein perspective," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1559-1573, August.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1559-1573
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    References listed on IDEAS

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    1. Sen, Pranab K. & Tsai, Ming-Tien & Jou, Yuh-Shan, 2007. "High-Dimension, LowSample Size Perspectives in Constrained Statistical Inference: The SARSCoV RNA Genome in Illustration," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 686-694, June.
    2. Tsai, Ming-Tien & Sen, Pranab Kumar, 2005. "Asymptotically optimal tests for parametric functions against ordered functional alternatives," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 37-49, July.
    3. Tzeng J-Y. & Byerley W. & Devlin B. & Roeder K. & Wasserman L., 2003. "Outlier Detection and False Discovery Rates for Whole-Genome DNA Matching," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 236-246, January.
    4. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
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