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Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies
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SYSNO ASEP 0435496 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies Author(s) Valenta, Zdeněk (UIVT-O) SAI, ORCID, RID
Kalina, Jan (UIVT-O) RID, SAI, ORCIDSource Title Biocybernetics and Biomedical Engineering. - : Elsevier - ISSN 0208-5216
Roč. 35, č. 1 (2015), s. 64-67Number of pages 4 s. Language eng - English Country PL - Poland Keywords Multivariate analysis ; Shrinkage ; Biased estimation ; Risk ; Squared-error loss ; Bias-variance trade-off Subject RIV BB - Applied Statistics, Operational Research Institutional support UIVT-O - RVO:67985807 UT WOS 000351328300007 EID SCOPUS 84922934166 DOI https://doi.org/10.1016/j.bbe.2014.10.004 Annotation Unbiased estimation appeared to be an accepted golden standard of statistical analysis ever until the Stein's discovery of a surprising phenomenon attributable to multivariate spaces. So called Stein's paradox arises in estimating the mean of a multivariate standard normal random variable. Stein showed that both natural and intuitive estimate of a multivariate mean given by the observed vector itself is not even admissible and may be improved upon under the squared-error loss when the dimension is greater or equal to three. Later Stein and his student James developed so called ‘James–Stein estimator’, a shrunken estimate of the mean, which had uniformly smaller risk for all values in the parameter space. The paradox first appeared both unintuitive and even unacceptable, but later it was recognised as one of the most influential discoveries of all times in statistical science. Today the ‘shrinkage principle’ literally permeates the statistical technology for analysing multivariate data, and in its application is not exclusively confined to estimating the mean, but also the covariance structure of multivariate data. We develop shrinkage versions of both the linear and quadratic discriminant analysis and apply them to sparse multivariate gene expression data obtained at the Centre for Biomedical Informatics (CBI) in Prague. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2015
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