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Copula modeling
Confidence interval example Stat 542
Peter Hoff
University of Washington
Copula modeling
Expression data from leukemia patients
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Confidence interval example Stat 542 Peter Hoff University of - - PowerPoint PPT Presentation
Confidence interval example Stat 542 Peter Hoff University of - - PowerPoint PPT Presentation
Copula modeling Confidence interval example Stat 542 Peter Hoff University of Washington Copula modeling Expression data from leukemia patients 10 8
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SLIDE 3
Copula modeling
Summary statistics
n<-dim(X)[1] ; p<-dim(X)[2] xbar<-apply(X,2,mean) Sig<-cov(X) > n [1] 143 > xbar [1] 6.598292 4.043136 > Sig [,1] [,2] [1,] 4.653583 3.076522 [2,] 3.076522 4.353581
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Copula modeling
Univariate tests and CIs
xint<-t.test(X[,1])$conf.int yint<-t.test(X[,2])$conf.int > xint [1] 6.241685 6.954900 > yint [1] 3.698214 4.388057
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Copula modeling
Univariate confidence region - not simultaneous
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4 6 8 10 12 2 4 6 8 10 X[,1] X[,2]
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6 7 8 2.5 3.5 4.5 5.5 X[,1] X[,2]
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Copula modeling
Simultaneous confidence ellipse
fq<-qf(c(.25,.5,.75,.9,.95),p,n-p) sc<- (n-1)*p/(n-p) # about p tq<- sc*fq Smh<-eigen(cov(X)/n) Smh<-Smh$vec%*%diag(sqrt(Smh$val))%*%t(Smh$vec) for(r in k) { theta<-seq(0,2*pi,length=100) z<-sqrt(r)*cbind(sin(theta),cos(theta)) x<- t( t(z%*%Smh)+xbar ) lines(x,col="green") }
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Copula modeling
Simultaneous confidence ellipse
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4 6 8 10 12 2 4 6 8 10 X[,1] X[,2]
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6 7 8 2.5 3.5 4.5 5.5 X[,1] X[,2]
SLIDE 8
Copula modeling
Simultaneous prediction ellipse
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