R/C-LE1.CS.R

In vrcp: Change Point Estimation for Regression with Varying Segments and Heteroscedastic Variances

# Linearizable C-LE1
# Common variance for both segments
# Smoothness

llsearch.LE1.CCS <- 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.LE1.CCS, 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.LE1.CCS <- function(j, x, y, n){
  a <- p.est.LE1.CCS(x,y,n,j)
  s2 <- a$sigma2
  return(p.ll.CCS(n, j, s2))
}

p.est.LE1.CCS <- function(x,y,n,j){
  xa <- x[1:j]
  ya <- y[1:j]
  jp1 <- j+1
  xb <- x[jp1:n]
  yb <- y[jp1:n]
  x1 <- x + (x[j]-x + exp(x)/exp(x[j])-1) * (x >= x[j])
 
  fun <- lm(y ~ x1) # points(x, predict(fun), type = "l", col = "red")
  
  a0 <- summary(fun)$coe[1]
  a1 <- summary(fun)$coe[2]
  b1 <- a1/exp(x[j])
  b0 <- a0+a1*x[j]-b1*exp(x[j])
  beta <-c(a0, a1, b0, b1)  
  s2<- (sum((ya-a0-a1*xa)^2)+sum((yb-b0-b1*exp(xb))^2))/n
  list(a0=beta[1],a1=beta[2],b0=beta[3],b1=beta[4],sigma2=s2,xj=x[j])
}

#  Function to compute the log-likelihood of the change-point problem

p.ll.CCS <- 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)
}