Abstract
Abstract C. R. Rao (1973, problem 5.11) constructed an example where a minimum variance unbiased estimator exists for the parameter function (1 – α)2 but no uniformly minimum variance unbiased estimator exists for α itself. The example was further discussed by Romano and Siegel (1986, example 9.6) who exhibited the family of unbiased estimators for α; the nonexistence of a uniformly minimum variance unbiased estimator comes from the fact that for a fixed value α0 of α the unbiased estimator with smallest variance depends on α0 and hence no unbiased estimator has uniformly smallest variance. In this note we show that a natural continuation of the example leads to an estimating equation for α that produces the maximum likelihood estimator. A second example, taken from Fisher (1958), exhibits a similar property. This example is both simpler and less artificial than the first, and we have found it very useful for teaching purposes. The general result is closely related to Fisher's motivation of maximum likeli...
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.