Statistical Estimation: Asymptotic Theory

When certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ..., X n be independent observations with the joint probability density !(x, O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0: ( X b ..., X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their…