Existence of the Minimum Variance Unbiased Estimator (MVUB) 1.2 2003/06/24 12:14:01 GMT-5 2003/07/10 10:36:59.432 GMT-5 Rob "The Kid" Nowak nowak@rice.edu Clayton Scott cscott@rice.edu Rob "The Kid" Nowak nowak@rice.edu Clayton Scott cscott@rice.edu Elizabeth Gregory lizzardg@rice.edu Jeffrey Silverman jsilv@rice.edu minimum variance unbiased estimator MVUB Does an MVUB estimator exist? Suppose there exist three unbiased estimators: θ 1 , θ 2 , and θ 3 . Two possibilities exist, as shown in and .

No MVUB estimator exists!

Finding the MVUB Estimator There is no simple, general procedure for finding the MVUB estimator. In the next several lectures we will discuss several approaches: Determine the so-called Cramer-Rao lowerbound (CRLB) and verify that the estimator achieves it. Apply the Rao-Blackwell theorem (we talked about this earlier in the course). Further restrict the estimator to a class of estimators (e.g., linear or polynomial functions of the data).

Outline of Remainder of Course The Cramer-Rao Lower Bound Linear Statistical Models Maximum Likelihood Estimation Bayesian Estimation Waveform Estimation - Wiener and Kalman Filters Adaptive Filtering