# Newton Raphson method for Example 1.6.5
y=c(6,5,4,6,6,3,12,7,4,2,6,7,4)
ybar=mean(y)
n=length(y)
sy=sum(y)
# no of iterations
iter=10
theta=rep(NA,iter)
U=rep(NA,iter)
Uprime=rep(NA,iter)
# newton raphson iterations
theta[1]=1.0
for (i in 2:iter)
{
U[i]= -n + (sy/theta[i-1])
Uprime[i]= -sy/(theta[i-1])^2
theta[i]= theta[i-1]- (U[i]/Uprime[i])
}
# Lets look at theta, U, Uprime
theta
U
Uprime
U/Uprime
# and approximate Standard error for the estimate is
se1=1/sqrt(-Uprime[iter])
#  Due to the form of U and U' in this example
# the Newton Raphson can also be obtained by
theta=rep(NA,iter)
theta[1]=0.5
for(i in 2:iter){theta[i]=2*theta[i-1]- (n/sum(y))*(theta[i-1]^2) }
#  The same as before but now using E(U') instead of U'
theta=rep(NA,iter)
U=rep(NA,iter)
Uprime=rep(NA,iter)
theta[1]=1.0
for (i in 2:iter)
{
U[i]= -n + (sy/theta[i-1])
Uprime[i]= -n/theta[i-1]
theta[i]= theta[i-1]- (U[i]/Uprime[i])
}
# Lets look again at theta, U, Uprime and se
theta
U
Uprime
U/Uprime
se2=1/sqrt(-Uprime[iter])
# why did it work so great with E(U')?