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 <- optim(xi,function(x){
y.xi <- y-x
a.y.xi <- t(outer(y.xi,a,'^'))
alp.a.y.xi <- as.numeric(t(alp)%*%a.y.xi)
return(-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))) )
},method= "BFGS")$par
y.xi <- y-xi
s <- sqrt(1/n*sum(s1*y.xi^2))
a.y.xi <- t(outer(y.xi,a,'^'))
s3.a.y.xi <- matrix(0,m,n)
for(i in 1:n)
s3.a.y.xi[,i] <- s3[i]*a.y.xi[,i]
alp <- solve(a.y.xi%*%t(a.y.xi))%*%rowSums(s3.a.y.xi)
alp.a.y.xi <- as.numeric(t(alp)%*%a.y.xi)
nu <- optim(nu,function(x){
-sum(log(2/s*x*exp(-abs(y.xi/s)^(2*x)/2)/(sqrt(2^(1/x))*gamma(1/(2*x)))*pnorm(alp.a.y.xi)))
},method="L-BFGS-B",lower=.01,upper=1)$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)
}
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