67 lines
2.8 KiB
R
67 lines
2.8 KiB
R
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#initialize model parameterss
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m<-100 #number of replications in simulation
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dim<-12 #dimension of random variable X
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truedim<-2 #dimension of B=b
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qs<-dim-truedim # dimension of orthogonal complement of B
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b1=c(1,1,1,1,1,1,0,0,0,0,0,0)/sqrt(6)
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b2=c(1,-1,1,-1,1,-1,0,0,0,0,0,0)/sqrt(6)
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b<-cbind(b1,b2)
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P<-b%*%t(b)
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sigma=0.5 #error standard deviation
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N<-200 #sample size
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K<-30 #number of arbitrary starting values for curvilinear optimization
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MAXIT<-50 #maximal number of iterations in curvilinear search algorithm
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##initailaize true covariancematrix of X
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Sig<-mat.or.vec(dim,dim)
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for (i in 1:dim){
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for (j in 1:dim){
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Sig[i,j]<-sigma^abs(i-j)
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}
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}
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Sroot<-chol(Sig)
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M1_JASA<-mat.or.vec(m,8)
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colnames(M1_JASA)<-c('CVE1','CVE2','CVE3','meanMAVE','csMAVE','phd','sir','save')
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#link function for M1
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fM1<-function(x){return(x[1]/(0.5+(x[2]+1.5)^2))}
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for (i in 1:m){
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#generate dat according to M1
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dat<-creat_sample_nor_nonstand(b,N,fM1,t(Sroot),sigma)
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#est sample covariance matrix
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Sig_est<-est_varmat(dat[,-1])
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#est trace of sample covariance matrix
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tr<-var_tr(Sig_est)
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#calculates Vhat_k for CVE1,CVE2, CVE3 for k=qs
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CVE1<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(0.8),tr=tr),maxit = MAXIT,sclack_para = 0)
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CVE2<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(2/3),tr=tr),maxit = MAXIT,sclack_para = 0)
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CVE3<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(0.5),tr=tr),maxit = MAXIT,sclack_para = 0)
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#calculate orthogonal complement of Vhat_k
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#i.e. CVE1$est_base[,1:truedim] is estimator for B with dimension (dim times (dim-qs))
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CVE1$est_base<-fill_base(CVE1$est_base)
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CVE2$est_base<-fill_base(CVE2$est_base)
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CVE3$est_base<-fill_base(CVE3$est_base)
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# calculate distance between true B and estimated B
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M1_JASA[i,1]<-subspace_dist(CVE1$est_base[,1:truedim],b)
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M1_JASA[i,2]<-subspace_dist(CVE2$est_base[,1:truedim],b)
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M1_JASA[i,3]<-subspace_dist(CVE3$est_base[,1:truedim],b)
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#meanMAVE
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mod_t2<-mave(Y~.,data=as.data.frame(dat),method = 'meanMAVE')
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M1_JASA[i,4]<-subspace_dist(mod_t2$dir[[truedim]],b)
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#csMAVE
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mod_t<-mave(Y~.,data=as.data.frame(dat),method = 'csMAVE')
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M1_JASA[i,5]<-subspace_dist(mod_t$dir[[truedim]],b)
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#phd
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test4<-summary(dr(Y~.,data=as.data.frame(dat),method='phdy',numdir=truedim+1))
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M1_JASA[i,6]<-subspace_dist(orth(test4$evectors[,1:truedim]),b)
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#sir
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test5<-summary(dr(Y~.,data=as.data.frame(dat),method='sir',numdir=truedim+1))
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M1_JASA[i,7]<-subspace_dist(orth(test5$evectors[,1:truedim]),b)
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#save
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test3<-summary(dr(Y~.,data=as.data.frame(dat),method='save',numdir=truedim+1))
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M1_JASA[i,8]<-subspace_dist(orth(test3$evectors[,1:truedim]),b)
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print(paste(i,paste('/',m)))
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}
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boxplot(M1_JASA[,]/sqrt(2*truedim),names=colnames(M1_JASA),ylab='err',main='M1')
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summary(M1_JASA[,])
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