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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F15%3A00435496%21RIV15-AV0-67985807
rdf:type
skos:Concept n16:Vysledek
dcterms:description
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. 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.
dcterms:title
Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies
skos:prefLabel
Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies Exploiting Stein's Paradox in Analysing Sparse Data from Genome-Wide Association Studies
skos:notation
RIV/67985807:_____/15:00435496!RIV15-AV0-67985807
n3:aktivita
n17:I
n3:aktivity
I
n3:cisloPeriodika
1
n3:dodaniDat
n7:2015
n3:domaciTvurceVysledku
n6:6423205 n6:6169899
n3:druhVysledku
n12:J
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n15:predkladatel
n3:idSjednocenehoVysledku
143
n3:idVysledku
RIV/67985807:_____/15:00435496
n3:jazykVysledku
n13:eng
n3:klicovaSlova
Multivariate analysis; Shrinkage; Biased estimation; Risk; Squared-error loss; Bias-variance trade-off
n3:klicoveSlovo
n4:Bias-variance%20trade-off n4:Biased%20estimation n4:Multivariate%20analysis n4:Squared-error%20loss n4:Risk n4:Shrinkage
n3:kodStatuVydavatele
PL - Polská republika
n3:kontrolniKodProRIV
[C062DD58AFDA]
n3:nazevZdroje
Biocybernetics and Biomedical Engineering
n3:obor
n11:BB
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n7:2015
n3:svazekPeriodika
35
n3:tvurceVysledku
Kalina, Jan Valenta, Zdeněk
s:issn
0208-5216
s:numberOfPages
4
n8:doi
10.1016/j.bbe.2014.10.004