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A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

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 this 
technique resides in the structure of an inner product space. The 
technique uses conditioning of an unbiased estimator on 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.