Nothing
R/REML.saery.AR1.R
In saery: Small Area Estimation for Rao and Yu Model
REML.saery.AR1 <-
function(X, ydi, D, md, sigma2edi, sigma1.0=1, sigma2.0=1, rho=0.5, MAXITER=20) {
rho.f <- rho
sigma1.f <- sigma1.0
sigma2.f <- sigma2.0
theta.f <- c(sigma1.f,sigma2.f,rho.f)
Bad <- 0
FLAG <- 0
p <- ncol(X)
a <- list(1:md[1])
mdcum <- cumsum(md)
for(d in 2:D)
a[[d]] <- (mdcum[d-1]+1):mdcum[d]
yd <- Xd <- list()
for(d in 1:D) {
yd[[d]] <- ydi[a[[d]]]
Xd[[d]] <- X[a[[d]],]
}
for(ITER in 1:MAXITER){
Vd.inv <- V1d <- V2d <- V3d <- VinvV1d <- VinvV2d <- VinvV3d <- Vinvyd <- VinvXd <- XtVinvV1dVinvX <- XtVinvV2dVinvX <- XtVinvV3dVinvX <-
VinvV1dVinvV1d <- VinvV2dVinvV2d <- VinvV3dVinvV3d <- XtVinvV1dVinvV1dVinvX <- VinvV1dVinvV2d <- VinvV1dVinvV3d <- VinvV2dVinvV3d <-
XtVinvV2dVinvV2dVinvX <- XtVinvV3dVinvV3dVinvX <- XtVinvV1dVinvV2dVinvX <- XtVinvV1dVinvV3dVinvX<- XtVinvV2dVinvV3dVinvX <- XtVinvV3dVinvV3dVinvX <-list()
Q.inv <- matrix(0, nrow=p, ncol=p)
tr.VinvV1d <- tr.VinvV2d <- tr.VinvV3d <- tr.VinvV1dVinvV1d <- tr.VinvV2dVinvV2d <- tr.VinvV3dVinvV3d <- tr.VinvV1dVinvV2d <- tr.VinvV1dVinvV3d <- tr.VinvV2dVinvV3d <- ytVinvX <- ytVinvV1dVinvy <- SumXtVinvV1dVinvX <- ytVinvV1dVinvX <- ytVinvV2dVinvy <- ytVinvV2dVinvX <- SumXtVinvV2dVinvX <- ytVinvV3dVinvy <- ytVinvV3dVinvX <- SumXtVinvV3dVinvX <- 0
for(d in 1:D) {
uno <- rep(1,md[d])
V1d[[d]] <- uno%*%t(uno)
Omegad <- matrix(0,nrow=md[d],ncol=md[d])
Omegad[lower.tri(Omegad)] <- rho.f^sequence((md[d]-1):1)
Omegad <- Omegad+t(Omegad)
diag(Omegad) <- 1
Omegad <- (1/(1-rho.f^2))*Omegad
V2d[[d]] <- Omegad
OmegadPrima <- matrix(0,nrow=md[d],ncol=md[d])
OmegadPrima[lower.tri(OmegadPrima)] <- sequence((md[d]-1):1)*rho.f^(sequence((md[d]-1):1)-1)
OmegadPrima <- OmegadPrima+t(OmegadPrima)
OmegadPrima <- (1/(1-rho.f^2))*OmegadPrima
OmegadPrima <- OmegadPrima + (2*rho.f/(1-rho.f^2))*Omegad
V3d[[d]] <- sigma2.f*OmegadPrima
Vd <- (sigma1.f *(uno%*%t(uno)) + sigma2.f * Omegad + diag(sigma2edi[a[[d]]]))
if(abs(det(Vd))<0.000000001 || abs(det(Vd))>10000000000) {
FLAG <- 1
Bad <- Bad+1
break
}
Vd.inv[[d]] <- solve(Vd)
Vinvyd[[d]] <- Vd.inv[[d]]%*%yd[[d]]
VinvXd[[d]] <- Vd.inv[[d]]%*%Xd[[d]]
Q.inv <- Q.inv + t(Xd[[d]])%*%VinvXd[[d]]
VinvV1d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]
tr.VinvV1d <- tr.VinvV1d + sum(diag(VinvV1d[[d]]))
XtVinvV1dVinvX[[d]]<- t(VinvXd[[d]])%*%V1d[[d]]%*%VinvXd[[d]]
ytVinvX <- ytVinvX + t(yd[[d]])%*%VinvXd[[d]]
ytVinvV1dVinvy <- ytVinvV1dVinvy + t(Vinvyd[[d]])%*%V1d[[d]]%*%Vinvyd[[d]]
ytVinvV1dVinvX <- ytVinvV1dVinvX + t(Vinvyd[[d]])%*%V1d[[d]]%*%VinvXd[[d]]
SumXtVinvV1dVinvX <- SumXtVinvV1dVinvX + XtVinvV1dVinvX[[d]]
VinvV2d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV2d <- tr.VinvV2d + sum(diag(VinvV2d[[d]]))
XtVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%VinvXd[[d]]
ytVinvV2dVinvy <- ytVinvV2dVinvy + t(Vinvyd[[d]])%*%V2d[[d]]%*%Vinvyd[[d]]
ytVinvV2dVinvX <- ytVinvV2dVinvX + t(Vinvyd[[d]])%*%V2d[[d]]%*%VinvXd[[d]]
SumXtVinvV2dVinvX <- SumXtVinvV2dVinvX + XtVinvV2dVinvX[[d]]
VinvV3d[[d]] <- Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV3d <- tr.VinvV3d + sum(diag(VinvV3d[[d]]))
XtVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V3d[[d]]%*%VinvXd[[d]]
ytVinvV3dVinvy <- ytVinvV3dVinvy + t(Vinvyd[[d]])%*%V3d[[d]]%*%Vinvyd[[d]]
ytVinvV3dVinvX <- ytVinvV3dVinvX + t(Vinvyd[[d]])%*%V3d[[d]]%*%VinvXd[[d]]
SumXtVinvV3dVinvX <- SumXtVinvV3dVinvX + XtVinvV3dVinvX[[d]]
VinvV1dVinvV1d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V1d[[d]]
tr.VinvV1dVinvV1d <- tr.VinvV1dVinvV1d + sum(diag(VinvV1dVinvV1d[[d]]))
XtVinvV1dVinvV1dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V1d[[d]]%*%VinvXd[[d]]
VinvV2dVinvV2d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV2dVinvV2d <- tr.VinvV2dVinvV2d + sum(diag(VinvV2dVinvV2d[[d]]))
XtVinvV2dVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]%*%VinvXd[[d]]
VinvV3dVinvV3d[[d]] <- Vd.inv[[d]]%*%V3d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV3dVinvV3d <- tr.VinvV3dVinvV3d + sum(diag(VinvV3dVinvV3d[[d]]))
XtVinvV3dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V3d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
VinvV1dVinvV2d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV1dVinvV2d <- tr.VinvV1dVinvV2d + sum(diag(VinvV1dVinvV2d[[d]]))
XtVinvV1dVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]%*%VinvXd[[d]]
VinvV1dVinvV3d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV1dVinvV3d <- tr.VinvV1dVinvV3d + sum(diag(VinvV1dVinvV3d[[d]]))
XtVinvV1dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
VinvV2dVinvV3d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV2dVinvV3d <- tr.VinvV2dVinvV3d + sum(diag(VinvV2dVinvV3d[[d]]))
XtVinvV2dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
}
if(FLAG==1){
FLAG<-0
ITER==MAXITER
break
}
Q <- solve(Q.inv)
tr.XtVinvV1dVinvXQ <- tr.XtVinvV2dVinvXQ <- tr.XtVinvV3dVinvXQ <- tr.XtVinvV1dVinvV1dVinvXQ <- tr.XtVinvV2dVinvV2dVinvXQ <- tr.XtVinvV3dVinvV3dVinvXQ <- tr.XtVinvV1dVinvV2dVinvXQ <- tr.XtVinvV1dVinvV3dVinvXQ <- tr.XtVinvV2dVinvV3dVinvXQ <- XtVinvV1dVinvXQ <- XtVinvV2dVinvXQ <- XtVinvV3dVinvXQ <- 0
for(d in 1:D){
tr.XtVinvV1dVinvXQ <- tr.XtVinvV1dVinvXQ + sum(diag(XtVinvV1dVinvX[[d]]%*%Q))
tr.XtVinvV2dVinvXQ <- tr.XtVinvV2dVinvXQ + sum(diag(XtVinvV2dVinvX[[d]]%*%Q))
tr.XtVinvV3dVinvXQ <- tr.XtVinvV3dVinvXQ + sum(diag(XtVinvV3dVinvX[[d]]%*%Q))
tr.XtVinvV1dVinvV1dVinvXQ <- tr.XtVinvV1dVinvV1dVinvXQ + sum(diag(XtVinvV1dVinvV1dVinvX[[d]]%*%Q))
XtVinvV1dVinvXQ <- XtVinvV1dVinvXQ + XtVinvV1dVinvX[[d]]%*%Q
tr.XtVinvV2dVinvV2dVinvXQ <- tr.XtVinvV2dVinvV2dVinvXQ + sum(diag(XtVinvV2dVinvV2dVinvX[[d]]%*%Q))
XtVinvV2dVinvXQ <- XtVinvV2dVinvXQ + XtVinvV2dVinvX[[d]]%*%Q
tr.XtVinvV3dVinvV3dVinvXQ <- tr.XtVinvV3dVinvV3dVinvXQ + sum(diag(XtVinvV3dVinvV3dVinvX[[d]]%*%Q))
XtVinvV3dVinvXQ <- XtVinvV3dVinvXQ + XtVinvV3dVinvX[[d]]%*%Q
tr.XtVinvV1dVinvV2dVinvXQ <- tr.XtVinvV1dVinvV2dVinvXQ + sum(diag(XtVinvV1dVinvV2dVinvX[[d]]%*%Q))
tr.XtVinvV1dVinvV3dVinvXQ <- tr.XtVinvV1dVinvV3dVinvXQ + sum(diag(XtVinvV1dVinvV3dVinvX[[d]]%*%Q))
tr.XtVinvV2dVinvV3dVinvXQ <- tr.XtVinvV2dVinvV3dVinvXQ + sum(diag(XtVinvV2dVinvV3dVinvX[[d]]%*%Q))
}
tr.XtVinvV1dVinvXQXtVinvV1dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV1dVinvXQ))
tr.XtVinvV2dVinvXQXtVinvV2dVinvXQ <- sum(diag(XtVinvV2dVinvXQ%*%XtVinvV2dVinvXQ))
tr.XtVinvV3dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV3dVinvXQ%*%XtVinvV3dVinvXQ))
tr.XtVinvV1dVinvXQXtVinvV2dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV2dVinvXQ))
tr.XtVinvV1dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV3dVinvXQ))
tr.XtVinvV2dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV2dVinvXQ%*%XtVinvV3dVinvXQ))
tr.PV1 <- tr.VinvV1d - tr.XtVinvV1dVinvXQ
tr.PV2 <- tr.VinvV2d - tr.XtVinvV2dVinvXQ
tr.PV3 <- tr.VinvV3d - tr.XtVinvV3dVinvXQ
tr.PV1PV1 <- tr.VinvV1dVinvV1d - 2*tr.XtVinvV1dVinvV1dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV1dVinvXQ
tr.PV2PV2 <- tr.VinvV2dVinvV2d - 2*tr.XtVinvV2dVinvV2dVinvXQ + tr.XtVinvV2dVinvXQXtVinvV2dVinvXQ
tr.PV3PV3 <- tr.VinvV3dVinvV3d - 2*tr.XtVinvV3dVinvV3dVinvXQ + tr.XtVinvV3dVinvXQXtVinvV3dVinvXQ
tr.PV1PV2 <- tr.VinvV1dVinvV2d - 2*tr.XtVinvV1dVinvV2dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV2dVinvXQ
tr.PV1PV3 <- tr.VinvV1dVinvV3d - 2*tr.XtVinvV1dVinvV3dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV3dVinvXQ
tr.PV2PV3 <- tr.VinvV2dVinvV3d - 2*tr.XtVinvV2dVinvV3dVinvXQ + tr.XtVinvV2dVinvXQXtVinvV3dVinvXQ
ytPV1Py <- ytVinvV1dVinvy - 2*ytVinvV1dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV1dVinvX%*%Q%*%t(ytVinvX)
ytPV2Py <- ytVinvV2dVinvy - 2*ytVinvV2dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV2dVinvX%*%Q%*%t(ytVinvX)
ytPV3Py <- ytVinvV3dVinvy - 2*ytVinvV3dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV3dVinvX%*%Q%*%t(ytVinvX)
S1 <- -0.5*tr.PV1 + 0.5*ytPV1Py
S2 <- -0.5*tr.PV2 + 0.5*ytPV2Py
S3 <- -0.5*tr.PV3 + 0.5*ytPV3Py
F11 <- 0.5*tr.PV1PV1
F22 <- 0.5*tr.PV2PV2
F33 <- 0.5*tr.PV3PV3
F12 <- 0.5*tr.PV1PV2
F13 <- 0.5*tr.PV1PV3
F23 <- 0.5*tr.PV2PV3
Ssig <- c(S1,S2,S3)
Fsig <- matrix(c(F11,F12,F13,F12,F22,F23,F13,F23,F33),ncol=3)
if(abs(det(Fsig))< 0.000000001 || sum(abs(Fsig))>10000000000) {
ITER <- MAXITER
Bad <- Bad+1
break
}
Fsig.inv <- solve(Fsig)
dif <- Fsig.inv%*%Ssig
theta.f <- theta.f + dif
rho.f <- theta.f[3,1]
sigma1.f <- theta.f[1,1]
sigma2.f <- theta.f[2,1]
if(identical(as.numeric(abs(dif)<0.00001),rep(1,3))) # Criterio de parada
break
}
if(sigma1.f<0 || sigma2.f<0 || rho.f< -1 || rho.f>1) {
ITER <- MAXITER
Bad <- Bad+1
}
return(list(as.vector(theta.f), Fsig, ITER, Bad, Q))
}
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REML.saery.AR1 <-
function(X, ydi, D, md, sigma2edi, sigma1.0=1, sigma2.0=1, rho=0.5, MAXITER=20) {
rho.f <- rho
sigma1.f <- sigma1.0
sigma2.f <- sigma2.0
theta.f <- c(sigma1.f,sigma2.f,rho.f)
Bad <- 0
FLAG <- 0
p <- ncol(X)
a <- list(1:md[1])
mdcum <- cumsum(md)
for(d in 2:D)
a[[d]] <- (mdcum[d-1]+1):mdcum[d]
yd <- Xd <- list()
for(d in 1:D) {
yd[[d]] <- ydi[a[[d]]]
Xd[[d]] <- X[a[[d]],]
}
for(ITER in 1:MAXITER){
Vd.inv <- V1d <- V2d <- V3d <- VinvV1d <- VinvV2d <- VinvV3d <- Vinvyd <- VinvXd <- XtVinvV1dVinvX <- XtVinvV2dVinvX <- XtVinvV3dVinvX <-
VinvV1dVinvV1d <- VinvV2dVinvV2d <- VinvV3dVinvV3d <- XtVinvV1dVinvV1dVinvX <- VinvV1dVinvV2d <- VinvV1dVinvV3d <- VinvV2dVinvV3d <-
XtVinvV2dVinvV2dVinvX <- XtVinvV3dVinvV3dVinvX <- XtVinvV1dVinvV2dVinvX <- XtVinvV1dVinvV3dVinvX<- XtVinvV2dVinvV3dVinvX <- XtVinvV3dVinvV3dVinvX <-list()
Q.inv <- matrix(0, nrow=p, ncol=p)
tr.VinvV1d <- tr.VinvV2d <- tr.VinvV3d <- tr.VinvV1dVinvV1d <- tr.VinvV2dVinvV2d <- tr.VinvV3dVinvV3d <- tr.VinvV1dVinvV2d <- tr.VinvV1dVinvV3d <- tr.VinvV2dVinvV3d <- ytVinvX <- ytVinvV1dVinvy <- SumXtVinvV1dVinvX <- ytVinvV1dVinvX <- ytVinvV2dVinvy <- ytVinvV2dVinvX <- SumXtVinvV2dVinvX <- ytVinvV3dVinvy <- ytVinvV3dVinvX <- SumXtVinvV3dVinvX <- 0
for(d in 1:D) {
uno <- rep(1,md[d])
V1d[[d]] <- uno%*%t(uno)
Omegad <- matrix(0,nrow=md[d],ncol=md[d])
Omegad[lower.tri(Omegad)] <- rho.f^sequence((md[d]-1):1)
Omegad <- Omegad+t(Omegad)
diag(Omegad) <- 1
Omegad <- (1/(1-rho.f^2))*Omegad
V2d[[d]] <- Omegad
OmegadPrima <- matrix(0,nrow=md[d],ncol=md[d])
OmegadPrima[lower.tri(OmegadPrima)] <- sequence((md[d]-1):1)*rho.f^(sequence((md[d]-1):1)-1)
OmegadPrima <- OmegadPrima+t(OmegadPrima)
OmegadPrima <- (1/(1-rho.f^2))*OmegadPrima
OmegadPrima <- OmegadPrima + (2*rho.f/(1-rho.f^2))*Omegad
V3d[[d]] <- sigma2.f*OmegadPrima
Vd <- (sigma1.f *(uno%*%t(uno)) + sigma2.f * Omegad + diag(sigma2edi[a[[d]]]))
if(abs(det(Vd))<0.000000001 || abs(det(Vd))>10000000000) {
FLAG <- 1
Bad <- Bad+1
break
}
Vd.inv[[d]] <- solve(Vd)
Vinvyd[[d]] <- Vd.inv[[d]]%*%yd[[d]]
VinvXd[[d]] <- Vd.inv[[d]]%*%Xd[[d]]
Q.inv <- Q.inv + t(Xd[[d]])%*%VinvXd[[d]]
VinvV1d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]
tr.VinvV1d <- tr.VinvV1d + sum(diag(VinvV1d[[d]]))
XtVinvV1dVinvX[[d]]<- t(VinvXd[[d]])%*%V1d[[d]]%*%VinvXd[[d]]
ytVinvX <- ytVinvX + t(yd[[d]])%*%VinvXd[[d]]
ytVinvV1dVinvy <- ytVinvV1dVinvy + t(Vinvyd[[d]])%*%V1d[[d]]%*%Vinvyd[[d]]
ytVinvV1dVinvX <- ytVinvV1dVinvX + t(Vinvyd[[d]])%*%V1d[[d]]%*%VinvXd[[d]]
SumXtVinvV1dVinvX <- SumXtVinvV1dVinvX + XtVinvV1dVinvX[[d]]
VinvV2d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV2d <- tr.VinvV2d + sum(diag(VinvV2d[[d]]))
XtVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%VinvXd[[d]]
ytVinvV2dVinvy <- ytVinvV2dVinvy + t(Vinvyd[[d]])%*%V2d[[d]]%*%Vinvyd[[d]]
ytVinvV2dVinvX <- ytVinvV2dVinvX + t(Vinvyd[[d]])%*%V2d[[d]]%*%VinvXd[[d]]
SumXtVinvV2dVinvX <- SumXtVinvV2dVinvX + XtVinvV2dVinvX[[d]]
VinvV3d[[d]] <- Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV3d <- tr.VinvV3d + sum(diag(VinvV3d[[d]]))
XtVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V3d[[d]]%*%VinvXd[[d]]
ytVinvV3dVinvy <- ytVinvV3dVinvy + t(Vinvyd[[d]])%*%V3d[[d]]%*%Vinvyd[[d]]
ytVinvV3dVinvX <- ytVinvV3dVinvX + t(Vinvyd[[d]])%*%V3d[[d]]%*%VinvXd[[d]]
SumXtVinvV3dVinvX <- SumXtVinvV3dVinvX + XtVinvV3dVinvX[[d]]
VinvV1dVinvV1d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V1d[[d]]
tr.VinvV1dVinvV1d <- tr.VinvV1dVinvV1d + sum(diag(VinvV1dVinvV1d[[d]]))
XtVinvV1dVinvV1dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V1d[[d]]%*%VinvXd[[d]]
VinvV2dVinvV2d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV2dVinvV2d <- tr.VinvV2dVinvV2d + sum(diag(VinvV2dVinvV2d[[d]]))
XtVinvV2dVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]%*%VinvXd[[d]]
VinvV3dVinvV3d[[d]] <- Vd.inv[[d]]%*%V3d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV3dVinvV3d <- tr.VinvV3dVinvV3d + sum(diag(VinvV3dVinvV3d[[d]]))
XtVinvV3dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V3d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
VinvV1dVinvV2d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]
tr.VinvV1dVinvV2d <- tr.VinvV1dVinvV2d + sum(diag(VinvV1dVinvV2d[[d]]))
XtVinvV1dVinvV2dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V2d[[d]]%*%VinvXd[[d]]
VinvV1dVinvV3d[[d]] <- Vd.inv[[d]]%*%V1d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV1dVinvV3d <- tr.VinvV1dVinvV3d + sum(diag(VinvV1dVinvV3d[[d]]))
XtVinvV1dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V1d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
VinvV2dVinvV3d[[d]] <- Vd.inv[[d]]%*%V2d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]
tr.VinvV2dVinvV3d <- tr.VinvV2dVinvV3d + sum(diag(VinvV2dVinvV3d[[d]]))
XtVinvV2dVinvV3dVinvX[[d]] <- t(VinvXd[[d]])%*%V2d[[d]]%*%Vd.inv[[d]]%*%V3d[[d]]%*%VinvXd[[d]]
}
if(FLAG==1){
FLAG<-0
ITER==MAXITER
break
}
Q <- solve(Q.inv)
tr.XtVinvV1dVinvXQ <- tr.XtVinvV2dVinvXQ <- tr.XtVinvV3dVinvXQ <- tr.XtVinvV1dVinvV1dVinvXQ <- tr.XtVinvV2dVinvV2dVinvXQ <- tr.XtVinvV3dVinvV3dVinvXQ <- tr.XtVinvV1dVinvV2dVinvXQ <- tr.XtVinvV1dVinvV3dVinvXQ <- tr.XtVinvV2dVinvV3dVinvXQ <- XtVinvV1dVinvXQ <- XtVinvV2dVinvXQ <- XtVinvV3dVinvXQ <- 0
for(d in 1:D){
tr.XtVinvV1dVinvXQ <- tr.XtVinvV1dVinvXQ + sum(diag(XtVinvV1dVinvX[[d]]%*%Q))
tr.XtVinvV2dVinvXQ <- tr.XtVinvV2dVinvXQ + sum(diag(XtVinvV2dVinvX[[d]]%*%Q))
tr.XtVinvV3dVinvXQ <- tr.XtVinvV3dVinvXQ + sum(diag(XtVinvV3dVinvX[[d]]%*%Q))
tr.XtVinvV1dVinvV1dVinvXQ <- tr.XtVinvV1dVinvV1dVinvXQ + sum(diag(XtVinvV1dVinvV1dVinvX[[d]]%*%Q))
XtVinvV1dVinvXQ <- XtVinvV1dVinvXQ + XtVinvV1dVinvX[[d]]%*%Q
tr.XtVinvV2dVinvV2dVinvXQ <- tr.XtVinvV2dVinvV2dVinvXQ + sum(diag(XtVinvV2dVinvV2dVinvX[[d]]%*%Q))
XtVinvV2dVinvXQ <- XtVinvV2dVinvXQ + XtVinvV2dVinvX[[d]]%*%Q
tr.XtVinvV3dVinvV3dVinvXQ <- tr.XtVinvV3dVinvV3dVinvXQ + sum(diag(XtVinvV3dVinvV3dVinvX[[d]]%*%Q))
XtVinvV3dVinvXQ <- XtVinvV3dVinvXQ + XtVinvV3dVinvX[[d]]%*%Q
tr.XtVinvV1dVinvV2dVinvXQ <- tr.XtVinvV1dVinvV2dVinvXQ + sum(diag(XtVinvV1dVinvV2dVinvX[[d]]%*%Q))
tr.XtVinvV1dVinvV3dVinvXQ <- tr.XtVinvV1dVinvV3dVinvXQ + sum(diag(XtVinvV1dVinvV3dVinvX[[d]]%*%Q))
tr.XtVinvV2dVinvV3dVinvXQ <- tr.XtVinvV2dVinvV3dVinvXQ + sum(diag(XtVinvV2dVinvV3dVinvX[[d]]%*%Q))
}
tr.XtVinvV1dVinvXQXtVinvV1dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV1dVinvXQ))
tr.XtVinvV2dVinvXQXtVinvV2dVinvXQ <- sum(diag(XtVinvV2dVinvXQ%*%XtVinvV2dVinvXQ))
tr.XtVinvV3dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV3dVinvXQ%*%XtVinvV3dVinvXQ))
tr.XtVinvV1dVinvXQXtVinvV2dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV2dVinvXQ))
tr.XtVinvV1dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV1dVinvXQ%*%XtVinvV3dVinvXQ))
tr.XtVinvV2dVinvXQXtVinvV3dVinvXQ <- sum(diag(XtVinvV2dVinvXQ%*%XtVinvV3dVinvXQ))
tr.PV1 <- tr.VinvV1d - tr.XtVinvV1dVinvXQ
tr.PV2 <- tr.VinvV2d - tr.XtVinvV2dVinvXQ
tr.PV3 <- tr.VinvV3d - tr.XtVinvV3dVinvXQ
tr.PV1PV1 <- tr.VinvV1dVinvV1d - 2*tr.XtVinvV1dVinvV1dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV1dVinvXQ
tr.PV2PV2 <- tr.VinvV2dVinvV2d - 2*tr.XtVinvV2dVinvV2dVinvXQ + tr.XtVinvV2dVinvXQXtVinvV2dVinvXQ
tr.PV3PV3 <- tr.VinvV3dVinvV3d - 2*tr.XtVinvV3dVinvV3dVinvXQ + tr.XtVinvV3dVinvXQXtVinvV3dVinvXQ
tr.PV1PV2 <- tr.VinvV1dVinvV2d - 2*tr.XtVinvV1dVinvV2dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV2dVinvXQ
tr.PV1PV3 <- tr.VinvV1dVinvV3d - 2*tr.XtVinvV1dVinvV3dVinvXQ + tr.XtVinvV1dVinvXQXtVinvV3dVinvXQ
tr.PV2PV3 <- tr.VinvV2dVinvV3d - 2*tr.XtVinvV2dVinvV3dVinvXQ + tr.XtVinvV2dVinvXQXtVinvV3dVinvXQ
ytPV1Py <- ytVinvV1dVinvy - 2*ytVinvV1dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV1dVinvX%*%Q%*%t(ytVinvX)
ytPV2Py <- ytVinvV2dVinvy - 2*ytVinvV2dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV2dVinvX%*%Q%*%t(ytVinvX)
ytPV3Py <- ytVinvV3dVinvy - 2*ytVinvV3dVinvX%*%Q%*%t(ytVinvX)+ytVinvX%*%Q%*%SumXtVinvV3dVinvX%*%Q%*%t(ytVinvX)
S1 <- -0.5*tr.PV1 + 0.5*ytPV1Py
S2 <- -0.5*tr.PV2 + 0.5*ytPV2Py
S3 <- -0.5*tr.PV3 + 0.5*ytPV3Py
F11 <- 0.5*tr.PV1PV1
F22 <- 0.5*tr.PV2PV2
F33 <- 0.5*tr.PV3PV3
F12 <- 0.5*tr.PV1PV2
F13 <- 0.5*tr.PV1PV3
F23 <- 0.5*tr.PV2PV3
Ssig <- c(S1,S2,S3)
Fsig <- matrix(c(F11,F12,F13,F12,F22,F23,F13,F23,F33),ncol=3)
if(abs(det(Fsig))< 0.000000001 || sum(abs(Fsig))>10000000000) {
ITER <- MAXITER
Bad <- Bad+1
break
}
Fsig.inv <- solve(Fsig)
dif <- Fsig.inv%*%Ssig
theta.f <- theta.f + dif
rho.f <- theta.f[3,1]
sigma1.f <- theta.f[1,1]
sigma2.f <- theta.f[2,1]
if(identical(as.numeric(abs(dif)<0.00001),rep(1,3))) # Criterio de parada
break
}
if(sigma1.f<0 || sigma2.f<0 || rho.f< -1 || rho.f>1) {
ITER <- MAXITER
Bad <- Bad+1
}
return(list(as.vector(theta.f), Fsig, ITER, Bad, Q))
}
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