1. Lecture 2 Interval Estimation
Dr. Hoda Ragab Rezk

2. Approximate Confidence Interval for Parameter with Maximum Likelihood Estimator (MLE)
Let X1,X2, ...,Xn be a random sample from a population X, with density f(x; θ). Let θ be the MLE of θ. If the sample size n is large, then using asymptotic property of the MLE as follows

3. where Var( θ ) denotes the variance of the estimator θ
where Var( θ ) denotes the variance of the estimator θ . Since, for large n, the MLE of θ is unbiased.
Remark
If Var( θ ) is not free of the parameter θ. We still use the same form of the confidence interval by replacing the parameter θ by θ in the expression of Var( θ ) .

9. Thank You