Nothing
MMeinfs_pca <- function(Y, ests = MMest_loccov(Y)) {
# empirical influences for MM-estimates + PCA estimates
# --------------------------------------------------------------------
rhobiweight <- function(x,c)
{
# Computes Tukey's biweight rho function with constant c for all values in x
hulp <- x^2/2 - x^4/(2*c^2) + x^6/(6*c^4)
rho <- hulp*(abs(x)<c) + c^2/6*(abs(x)>=c)
return(rho)
}
# --------------------------------------------------------------------
rhobiweightder1 <- function(x,c)
{
# Computes Tukey's biweight psi function with constant c for all values in x
hulp <- x - 2*x^3/(c^2) + x^5/(c^4)
rho <- hulp*(abs(x)<c)
return(rho)
}
# --------------------------------------------------------------------
rhobiweightder2 <- function(x,c)
{
# Computes derivative of Tukey's biweight psi function with constant c for all values in x
hulp <- 1 - 6*x^2/(c^2) + 5*x^4/(c^4)
rho <- hulp*(abs(x)<c)
return(rho)
}
# --------------------------------------------------------------------
vecop <- function(mat) {
# performs vec-operation (stacks colums of a matrix into column-vector)
nr <- nrow(mat)
nc <- ncol(mat)
vecmat <- rep(0,nr*nc)
for (col in 1:nc) {
startindex <- (col-1)*nr+1
vecmat[startindex:(startindex+nr-1)] <- mat[,col]
}
return(vecmat)
}
# --------------------------------------------------------------------
# - main function -
# --------------------------------------------------------------------
n <- nrow(Y)
p <- ncol(Y)
c0 <- ests$c0
b <- ests$b
c1 <- ests$c1
MMloc <- ests$Mu
MMcov <- ests$Sigma
MMGamma <- det(MMcov)^(-1/p) * MMcov
# compute eigenvalues/vectors
eigresGamma <- eigen(MMGamma)
IXGamma <- order(eigresGamma$values)
eigs <- eigresGamma$values[IXGamma]
eigvecs <- eigresGamma$vectors[,IXGamma]
for (k in 1:p) {
IX <- order(abs(eigvecs[,k]))
eigvecs[,k] <- sign(eigvecs[IX[p],k]) * eigvecs[,k]
}
varperc <- rep(0,p-1)
for (k in 1:(p-1)) {
varperc[k] <- sum(eigs[(p-k+1):p]) / sum(eigs)
}
divec <- sqrt(mahalanobis(Y, MMloc, MMcov))
psidervec <- rhobiweightder2(divec, c1)
psidervecS <- rhobiweightder2(divec, c0)
uvec <- rhobiweightder1(divec, c1) / divec
uvecS <- rhobiweightder1(divec, c0) / divec
vvec <- rhobiweightder1(divec,c1) * divec
vvecS <- rhobiweightder1(divec,c0) * divec
rhovecS <- rhobiweight(divec,c0)
betaMM <- (1-1/p) * mean(uvec) + 1/p * mean(psidervec)
einfsloc <- 1 / betaMM * matrix(rep(uvec,p), ncol=p) * (Y - matrix(rep(MMloc,n), n, byrow=TRUE))
betaS <- (1-1/p) * mean(uvecS) + 1/p * mean(psidervecS)
einfslocS <- 1 / betaS * matrix(rep(uvecS,p), ncol=p) * (Y - matrix(rep(MMloc,n), n, byrow=TRUE))
gamma3 <- mean(vvecS)
gamma1MM <- mean(psidervec * (divec^2) + (p+1) * vvec) / (p+2)
gamma1S <- mean(psidervecS * (divec^2) + (p+1) * vvecS) / (p+2)
einfscov <- matrix(0,n,p*p)
einfscovS <- matrix(0,n,p*p)
einfsshape <- matrix(0,n,p*p)
einfseigvec <- matrix(0,n,p*p)
einfseigscov <- matrix(0,n,p)
einfseigs <- matrix(0,n,p)
einfsvarperc <- matrix(0,n,p-1)
for (i in 1:n) {
IFcov <- 2/gamma3 * (rhovecS[i] - b) * MMcov + 1/gamma1MM * p * vvec[i] * (t(Y[i,]-MMloc) %*% (Y[i,]-MMloc) / divec[i]^2 - 1/p * MMcov)
einfscov[i,] <- vecop( IFcov )
IFcovS <- 2/gamma3 * (rhovecS[i] - b) * MMcov + 1/gamma1S * p * vvecS[i] * (t(Y[i,]-MMloc) %*% (Y[i,]-MMloc) / divec[i]^2 - 1/p * MMcov)
einfscovS[i,] <- vecop( IFcovS )
IFshape <- 1/gamma1MM * p * vvec[i] * det(MMcov)^(-1/p) * (t(Y[i,]-MMloc) %*% (Y[i,]-MMloc) / divec[i]^2 - 1/p * MMcov)
einfsshape[i,] <- vecop( IFshape )
IFeigvecs <- matrix(0,p,p)
for (k in 1:p) {
IFeigveck <- rep(0,p)
for (j in 1:p) {
if (j != k) {
IFeigveck <- IFeigveck + 1 / (eigs[k]-eigs[j]) * (t(eigvecs[,j]) %*% IFshape %*% eigvecs[,k]) %*% eigvecs[,j]
}
}
IFeigvecs[,k] <- IFeigveck
einfseigs[i,k] <- t(eigvecs[,k]) %*% IFshape %*% eigvecs[,k]
einfseigscov[i,k] <- t(eigvecs[,k]) %*% IFcov %*% eigvecs[,k]
}
einfseigvec[i,] <- vecop(IFeigvecs)
for (k in 1:(p-1)) {
einfsvarperc[i,k] <- 1 / sum(eigs) * ((1-varperc[k]) * sum(einfseigs[i,(p-k+1):p]) - varperc[k] * sum(einfseigs[i,1:(p-k)]))
}
}
return(list(loc=einfsloc, locS=einfslocS, shape=einfsshape, cov=einfscov, covS=einfscovS, eigvec=einfseigvec, eigs=einfseigs, eigscov=einfseigscov, varperc=einfsvarperc))
}
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