inst/scripts/Estimation/emp_ml.R

In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

## "Statistical foundations of machine learning" software
## R package gbcode 
## Author: G. Bontempi

# Script: shows the use of maximum likelihood for parameter estimation



eml <- function(m,D,var) {   ## empirical likelihood function (1 argument)
  
  N<- length(D)
  Lik<-1
  for (i in 1:N)
  {
    Lik<-Lik*dnorm(D[i],m,sqrt(var))
    
  }
  -log(Lik)
}

eml2 <- function(m,D) {   ## empirical likelihood function (2 arguments)
  N<- length(D)
  Lik<-1
  for (i in 1:N)
    Lik<-Lik*dnorm(D[i],m[1],sqrt(max(0,m[2])))
  -log(Lik)
}

N <-20

DN<-rnorm(N) # data generation

xmin<-optimize( eml,c(-10,10),D=DN,var=1,lower=-1,upper=1)
# maximization of log likelihood function (1 argument)
cat("Mean ML estimation=",xmin$minimum,"\n")

xmin2<-optim( c(-10,10),eml2, D=DN)
# maximization of log likelihood function (2 arguments: mean and variance)

cat("Mean and variance ML estimation=",xmin2$par,"\n")

mean(DN) ## sample average
var(DN)*(N-1)/N ## sample mean with N at the denominator