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#############################################################
#
# varComprob.MM function
# Author: Claudio Agostinelli and Victor J. Yohai
# E-mail: claudio@unive.it
# Date: June 24, 2014
# Version: 0.1
#
# Copyright (C) 2014 Claudio Agostinelli
# and Victor J. Yohai
#
#############################################################
varComprob.MM <- function(y, x, V, S=NULL, beta=NULL, gamma=NULL, scale=NULL, control=varComprob.control()) {
# y: matrix. dim(y)=c(p,n)
# x: array. dim(x)=c(p,n,k)
# V: array. dim(V)=c(p,p,R)
# beta: vector or NULL. length(beta)=k
# gamma: vector or NULL. length(gamma)=R
# scale: scalar or NULL.
## SET STORAGE MODE OF y, x and V
storage.mode(y) <- "double"
storage.mode(x) <- "double"
storage.mode(V) <- "double"
xdim <- dim(x)
p <- xdim[1]
n <- xdim[2]
k <- xdim[3]
Vdim <- dim(V)
R <- Vdim[3]
JL <- p*(p-1)/2
## About initial values
if (is.null(beta))
beta <- S$beta
if (is.null(gamma))
gamma <- S$gamma
if (is.null(scale))
scale <- S$scale
if(is.null(beta) | is.null(gamma) | is.null(scale))
stop('Initial values for beta, gamma and value for the scale must be supplied')
v <- qchisq(seq(0.0001,0.9999,length=5000), p)
if (control$psi!="rocke")
s0 <- doSstep(m=v, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
else
s0 <- doSsteprocke(m=v, scale=1, bb=control$bb, p=p, arp=control$arp.chi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
##BEGIN# Iterations
iter <- 0
dbeta <- control$rel.tol.beta+1
dgamma <- control$rel.tol.gamma+1
while ((max(dbeta) > control$rel.tol.beta | dgamma > control$rel.tol.gamma) & iter < control$max.it) {
iter <- iter+1
## SIGMA
Sigma <- Vprod(V=V, gamma=gamma)
Sigmastar <- Sigma/det(Sigma)^(1/nrow(Sigma))
Sigmastarinv <- solve(Sigmastar)
## RESIDUALS
if (k==0) {
rr <- y
beta <- beta1 <- vector(mode="numeric", length=0)
control$cov <- FALSE
} else
rr <- vcrobresid(y=y, x=x, beta=beta)
## SQUARED MAHALANOBIS DISTANCES
RR <- rep(0, n)
for (i in 1:n)
RR[i] <- drop(rr[,i]%*%Sigmastarinv%*%rr[,i])
## WEIGHTS
if (control$psi!="rocke")
W <- vcrobweights(m=RR, scale=scale, cc=control$tuning.psi, psi=control$psi)
else
W <- vcrobweightsrocke(m=RR, scale=scale, p=p, arp=control$arp.psi)
## SQUARED MAHALANOBIS DISTANCES
if (k > 0) {
XX <- matrix(0, nrow=k, ncol=k)
XY <- matrix(0, nrow=k, ncol=1)
for (i in 1:n) {
XX <- XX + W[i]*t(x[,i,])%*%Sigmastarinv%*%x[,i,]
XY <- XY + W[i]*t(x[,i,])%*%Sigmastarinv%*%y[,i]
}
## BETAS
beta1 <- drop(solve(XX)%*%XY)
dbeta <- max(abs(beta-beta1))
} else
dbeta <- 0
## GAMMAS
Mmax <- doGammaClassicMMGoal(x=gamma, resid=rr, scale=scale, V=V, Mmax=NA, controllo=control)+10
if (is.na(Mmax))
stop("The Sigma matrix is singular and we do not know how to fix it")
gamma1 <- drop(doGammaClassicMMstep(gamma=gamma, resid=rr, scale=scale, V=V, Mmax=Mmax, control=control))
dgamma <- max(abs(gamma1-gamma))
if (iter > control$max.it/2) {
beta <- (beta1+beta)/2
gamma <- (gamma1+gamma)/2
} else {
beta <- beta1
gamma <- gamma1
}
if (control$trace.lev>1) {
cat('Iterations: ', iter, '\n')
cat('beta: ', beta, '\n')
cat('gamma: ', gamma, '\n')
M <- doGammaClassicMMGoal(x=gamma, resid=rr, scale=scale, V=V, Mmax=Mmax, controllo=control)
cat('M: ', M, '\n')
cat('diff max(abs(beta_i - beta_i+1)): ', dbeta, '\n')
cat('diff max(abs(gamma_i - gamma_i+1)): ', dgamma, '\n')
}
}
##END# Iterations
##BEGIN# Eta0
Sigma <- Vprod(V=V, gamma=gamma)
Sigmainv <- solve(Sigma)
RSR <- rep(0, ncol(rr))
for (i in 1:ncol(rr))
RSR[i] <- drop(rr[,i]%*%Sigmainv%*%rr[,i])
if (control$psi!="rocke")
eta0 <- doSstep(m=RSR/s0, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
else
eta0 <- doSsteprocke(m=RSR/s0, scale=1, bb=control$bb, p=p, arp=control$arp.chi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
##END# Eta0
##BEGIN# VCOV
vcov <- VCOV.ClassicMM(beta=beta, gamma=gamma, scale=scale, y=y, x=x, V=V, control=control)
vcov.beta <- vcov[1:k,1:k]
vcov.gamma <- vcov[(k+1):(k+R),(k+1):(k+R)]
##END# VCOV
result <- list()
result$call <- match.call()
result$beta <- drop(beta)
result$vcov.beta <- vcov.beta
result$eta <- drop(gamma*eta0)
result$vcov.eta <- vcov.gamma*eta0^2
result$gamma <- drop(gamma)
result$vcov.gamma <- vcov.gamma
result$eta0 <- eta0
result$resid <- rr
result$weights <- W
result$scales <- scale
result$scale0 <- s0
result$min <- doGammaClassicMMGoal(x=gamma, resid=rr, scale=scale, V=V, Mmax=NA, controllo=control)
result$iterations <- iter
result$control <- control
result$control$method <- "MM"
class(result) <- 'varComprob.MM'
return(result)
}
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