bootSVD (version 0.1)

reindexPCsByK: Allows for calculation of low dimensional standard errors & percentiles, by re-indexing the $A^b$ by PC index ($k$) rather than bootstrap index ($b$).

Description

This function is used as a precursor step for calculate bootstrap standard errors, or percentiles. For very high dimensional data, we recommend that the this function be applied to the low dimensional components $A^b$, but the function can also be used to reorder a list of high dimensional bootstrap PCs. In general, we recommend that as many operations as possible be applied to the low dimensional components, as opposed to their high dimensional counterparts. This function is called by getMomentsAndMomentCI.

Usage

reindexPCsByK(PCsByB)

Arguments

PCsByB

a B-length list of (r by K) bootstrap PCs matrices for each bootstrap sample, where K is the number of PCs of interest and B is the number of bootstrap samples. These may refer to th

Value

• a K-length list of ($B$ by $r$) PC matrices. If PCsByK is the output of reindexPCsByK, then PCsByK[[k]][b,] is the $k^{th}$ fitted PC from the b^{th} bootstrap sample. This allows for quick estimation of low dimensional moments, or percentiles. Moments can also be directly calculated by the getMomentsAndMomentCI function.

Examples

#use small n, small B for a quick illustration
set.seed(0)
Y<-simEEG(n=100, centered=TRUE, wide=TRUE)
svdY<-fastSVD(Y)
V<- svdY$v #original sample PCs
DUt<- tcrossprod(diag(svdY$d),svdY$u)
bInds<-genBootIndeces(B=200,n=dim(DUt)[2])
bootSVD_LD_output<-bootSVD_LD(DUt=DUt,bInds=bInds,K=3,talk=TRUE)

########
# to get 'low dimensional PC' moments and lower percentiles
AsByB<-bootSVD_LD_output$As
AsByK<-reindexPCsByK(AsByB)

meanA1<-	apply(AsByK[[1]],2,mean)
seA1<-	apply(AsByK[[1]],2,sd)
pA1<-	apply(AsByK[[1]],2,function(x) quantile(x,.05))
#can also use lapply to get a list (indexed by k=1,...K) of
#the means, standard errors, or percentiles for each PC.
#See example below, for high dimensional bootstrap PCs.

#Alternatively, moments can be calculated with
seA1_v2<- getMomentsAndMomentCI(As=AsByB,
		V=diag(dim(AsByB[[1]])[1]))$sdPCs[[1]]
all(seA1_v2==seA1)

#Additional examples of exploring the low dimensional bootstrap
#PC distribution are given in the documentation for
#the 'bootSVD' function.
#########

#########
#High dimensional percentiles for each PC
VsByB<-As2Vs(As=AsByB,V=V)
VsByK<-reindexPCsByK(VsByB)
percentileCI_Vs<-lapply(VsByK,function(mat_k){
	apply(mat_k,2,function(x) quantile(x,c(.025,.975)))
})
k=2 # the 2nd PC is a little more interesting here.
matplot(t(percentileCI_Vs[[k]]),type='l',lty=1,col='blue')
lines(V[,k])
########