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

Ming-Tien Tsai and Pranab Kumar Sen

Journal of Multivariate Analysis, 2010, vol. 101, issue 7, 1559-1573

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.

Keywords: Chen-Stein; Theorem; Hamming-Shannon; pooled; measure; Lorenz; ordering; Ordered; alternatives; Permutation; jackknife; Subgroup; decomposability; Union-intersection; principle (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00054-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:101:y:2010:i:7:p:1559-1573

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().