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# Linear U-QE2
# Common variance for both segments
llsearch.QE2.C <- function(x, y, n, jlo, jhi)
{
fj <- matrix(0, n)
fxy <- matrix(0, jhi - jlo + 1)
jgrid <- expand.grid(jlo:jhi)
k.ll <- apply(jgrid, 1, p.estFUN.QE2.C, x = x, y = y, n = n)
fxy <- matrix(k.ll, nrow = jhi-jlo+1)
rownames(fxy) <- jlo:jhi
z <- findmax(fxy)
jcrit <- z$imax + jlo - 1
list(jhat = jcrit, value = max(fxy))
}
# Function for deriving the ML estimates of the change-points problem.
p.estFUN.QE2.C <- function(j, x, y, n){
a <- p.est.QE2.C(x,y,n,j)
s2 <- a$sigma2
return(p.ll.C(n, j, s2))
}
p.est.QE2.C <- function(x,y,n,j){
xa <- x[1:j]
ya <- y[1:j]
jp1 <- j+1
xb <- x[jp1:n]
yb <- y[jp1:n]
g1 <- lm(ya ~ xa++I(xa^2))
g2 <- lm(yb ~ log(xb))
beta <-c(g1$coef[1],g1$coef[2],g1$coef[3],g2$coef[1],g2$coef[2])
s2 <- (sum((ya-g1$fit)^2)+sum((yb-g2$fit)^2))/n
list(a0=beta[1],a1=beta[2],a2=beta[3],b0=beta[4],b1=beta[5],sigma2=s2,xj=x[j])
}
# Function to compute the log-likelihood of the change-point problem
p.ll.C <- function(n, j, s2){
q1 <- n * log(sqrt(2 * pi))
q2 <- 0.5 * n * (1 + log(s2))
- (q1 + q2)
}
findmax <-function(a)
{
maxa<-max(a)
imax<- which(a==max(a),arr.ind=TRUE)[1]
jmax<-which(a==max(a),arr.ind=TRUE)[2]
list(imax = imax, jmax = jmax, value = maxa)
}
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