Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Estimation of Gini-Simpson index for SNP data

  • Kang, Joonsung (Department of Information Statistics, Gangneung-Wonju National University)
  • Received : 2017.09.29
  • Accepted : 2017.11.01
  • Published : 2017.11.30
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Abstract

We take genomic sequences of high-dimensional low sample size (HDLSS) without ordering of response categories into account. When constructing an appropriate test statistics in this model, the classical multivariate analysis of variance (MANOVA) approach might not be useful owing to very large number of parameters and very small sample size. For these reasons, we present a pseudo marginal model based upon the Gini-Simpson index estimated via Bayesian approach. In view of small sample size, we consider the permutation distribution by every possible n! (equally likely) permutation of the joined sample observations across G groups of (sizes $n_1,{\ldots}n_G$). We simulate data and apply false discovery rate (FDR) and positive false discovery rate (pFDR) with associated proposed test statistics to the data. And we also analyze real SARS data and compute FDR and pFDR. FDR and pFDR procedure along with the associated test statistics for each gene control the FDR and pFDR respectively at any level ${\alpha}$ for the set of p-values by using the exact conditional permutation theory.

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