R/FGSEPN.EM.R

In a-mahdavi/Alt.EM:

FGSEPN.EM <- function(y, xi, s, la, nu, iter.max=200, tol=10^-6){  
	m <- length(la) ; a=seq(1,2*m-1,by=2)
	n <- length(y)
        dif <- 1
        count <- 0
	alp <- as.matrix(la/s^a)
	y.xi <- y-xi
	a.y.xi <- t(outer(y.xi,a,'^')) 
	alp.a.y.xi <- as.numeric(t(alp)%*%a.y.xi)
	while ((dif > tol) && (count <= iter.max)) {
# E step
	s1 <- nu*abs(y.xi/s)^(2*nu-2)
	s3 <- alp.a.y.xi + dnorm(alp.a.y.xi)/pnorm(alp.a.y.xi)
	LL <- sum(log(2/s*nu*exp(-abs(y.xi/s)^(2*nu)/2)/(sqrt(2^(1/nu))*gamma(1/(2*nu)))*pnorm(alp.a.y.xi))) # log-likelihood function
# MCE steps
	xi <-  uniroot(function(x){
	y.xi <- y-x
	a.y.xi <- t(outer(y.xi,a,'^'))
	b.y.xi <- t(outer(y.xi,a-1,'^')) 
	b.y.xi <- apply(b.y.xi,2,function(x) a*x)
	alp.a.y.xi <- as.numeric(t(alp)%*%a.y.xi)
	alp.b.y.xi <- as.numeric(t(alp)%*%b.y.xi)
	return(1/s^2*sum(s1*y.xi)+sum((alp.a.y.xi)*(alp.b.y.xi))-sum(s3*alp.b.y.xi))
		},c(xi-50,xi+50))$root
	y.xi <- y-xi 
	s <- sqrt(1/n*sum(s1*y.xi^2))
	a.y.xi <- t(outer(y.xi,a,'^')) 
	s3.a.y.xi <- matrix(0,m,n)
	for(i in 1:n)
	s3.a.y.xi[,i] <- s3[i]*a.y.xi[,i]
	alp <- solve(a.y.xi%*%t(a.y.xi))%*%rowSums(s3.a.y.xi)
	alp.a.y.xi <- as.numeric(t(alp)%*%a.y.xi)
	nu <- optim(nu,function(x){
		-sum(log(2/s*x*exp(-abs(y.xi/s)^(2*x)/2)/(sqrt(2^(1/x))*gamma(1/(2*x)))*pnorm(alp.a.y.xi)))
	},method="L-BFGS-B",lower=.01,upper=1)$par
	LL.new <- sum(log(2/s*nu*exp(-abs(y.xi/s)^(2*nu)/2)/(sqrt(2^(1/nu))*gamma(1/(2*nu)))*pnorm(alp.a.y.xi))) # log-likelihood function
	count <- count +1 
	dif <- abs(LL.new/LL-1)
	}
	aic <- -2 * LL.new + 2 * (2+m+1)
	bic <- -2 * LL.new + log(n) * (2+m+1)
list(xi=xi, sigma=s, la=alp*s^a, nu=nu, loglik=LL.new, AIC=aic, BIC=bic, iter=count)
}