Theory and Methods of Statistics

5

Point Estimation in Parametric Models

Abstract

A function $g\left(\theta \right)$ of a parameter θ in a parametric family of distributions is to be estimated from a random sample. Methods of constructing Uniformly Minimum Variance Unbiased Estimators and Minimum Risk Equivariant Estimators are developed. Lower bounds for the variance of unbiased estimators is derived, which leads to the concept of Fisher-Information. Several methods of estimation, especially the Method of Maximum Likelihood, are introduced.

Keywords

UMVUE; MRE Estimator; Fisher Information; Methods of Estimation

5.1 Optimality Under Unbiasedness, Squared-Error Loss, UMVUE

In the general framework ...