Thread: Parameter estimation

Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

I'm not sure how to proceed from here.

Originally Posted by BrownianMan

Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

I'm not sure how to proceed from here.

With method of moments, the game is to equate the empirical moments with the theoretical moments. Set Xbar = p, then just plug that in to get the estimate of theta.

So would the answer be -0.08?

use p-hat as 9/20 to estimate p in theta

ln (.45/.55)

Thanks, I got it!

The next part of the question which I'm not sure of is:

Obtain a 95% confidence interval for theta based on the MLE of theta.