STAT 463 Lecture Notes - Lecture 3: Beak, Meke, Exponential Family
Document Summary
For a particular estimation problem there may be several (maybe even many) competing estimators. Right o , we acknowledge that some estimators are indeed better than others. , xn poisson( ) we have two competing estimators for : x and s2 (why?). It turns out that x is a better estimator than is s2. To see why, we"ll start by discussing some properties of estimators that will help us decide which are better. An estimator b is an unbiased estimator of if: In addition to being unbiased, a good estimator has small variance. If b 1 and b 2 are unbiased estimators of , then b 1 is a better estimator (or, a more e cient estimator) than b 2 if: Remember that estimators are statistics, and are themselves rvs. Let b be an estimator for a parameter . An estimator whose bias is 0 (i. e. , e(b ) = ) is an unbiased estimator for .
