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.
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Marengo, J.E. and Farnsworth, D.L. (2021) A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators. Open Journal of Statistics, 11, 437-442. https://doi.org/10.4236/ojs.2021.113027
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