Statistical Inference ( Unit 2: Cramer-Rao Inequality, Method Of Moment, Maximum Likelihood Estimator)
Changing Color Blog Name Statistical Inference I: (Cramer-Rao Inequality, Method Of Moment, Maximum Likelihood Estimator) I. Introduction We see in unbiased estimator from two distinct unbiased estimators give infinitely many unbiased estimators of θ, among these estimators we find the best estimator for parameter θ by comparing their variance or mean square errors. But in some examples, we see that the number of estimators is possible as. For Normal distribution: If X1, X2, ........Xn. random sample from a normal distribution with mean 𝛍 and variance 𝛔², then T1 = x̄, T2 = Sample median, both are unbiased estimators for parameter 𝛍. Now we find a sufficient estimator; therefore, T1 is a sufficient estimator for 𝛍, hence it is the best estimator for parameter 𝛍. Thus, for finding the best estimator, we check if the estimator is sufficient or not. Now we are interested in finding the variance of th