Properties
Asymptotic Properties
Interval Estimation
Maximum Likelihood Estimation
Bernoulli example
Properties
Fisher’s information (Fisher information - Wikipedia):
Check Section 4.2.5 of the textbook for a complete derivation.
Optimization in MLE
Normal
norm.data <- rnorm(100,1,2)
normal.lik<-function(theta,y){
mu <- theta[1]
sigma2 <- theta[2]
n <- length(y)
logl<- -n/2*log(2*pi) -n/2*log(sigma2) - (2*sigma2)^(-1)*sum((y-mu)^2)
return(-logl)
}
optim(c(0,1),normal.lik,y=norm.data,method="BFGS")
$par
[1] 0.9078143 4.1350937
$value
[1] 212.8693
$counts
function gradient
34 15
$convergence
[1] 0
$message
NULL
Exercises
