TITLE:
A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators
AUTHORS:
James E. Marengo, David L. Farnsworth
KEYWORDS:
Conditional Variance Formula, Conditioning, Geometric Representation, Minimum Variance Estimator, Rao-Blackwell Theorem, Sufficient Statistic, Unbiased Estimator
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.3,
June
25,
2021
ABSTRACT: 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.