%0 Journal Article
%T A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators
%A James E. Marengo
%A David L. Farnsworth
%J Open Journal of Statistics
%P 437-442
%@ 2161-7198
%D 2021
%I Scientific Research Publishing
%R 10.4236/ojs.2021.113027
%X Our purpose is twofold: to present
a prototypical example of the conditioning technique to obtain the best
estimator of a parameter and to show that th</span><span style=\"font-family:Verdana;\">is
technique resides in the structure of an inner product space. Th</span><span style=\"font-family:Verdana;\">e
technique uses conditioning </span></span><span style=\"font-family:Verdana;\">of</span><span style=\"font-family:Verdana;\"> an unbiased estimator </span><span style=\"font-family:Verdana;\">on</span><span style=\"font-family:Verdana;\"> a sufficient statistic. This procedure is founded upon the conditional
variance formula, which leads to an inner product space and a geometric
interpretation. The example clearly illustrates the dependence on the sampling
methodology. These advantages show the power and centrality of this process.
%K Conditional Variance Formula
%K Conditioning
%K Geometric Representation
%K Minimum Variance Estimator
%K Rao-Blackwell Theorem
%K Sufficient Statistic
%K Unbiased Estimator
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=110122