A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators - Open Journal of Statistics

OJS > Vol.11 No.3, June 2021

Open Journal of Statistics

Volume 11, Issue 3 (June 2021)

ISSN Print: 2161-718X ISSN Online: 2161-7198

Google-based Impact Factor: 1.45 Citations

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

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DOI: 10.4236/ojs.2021.113027 330 Downloads 1,902 Views Citations

Author(s)

James E. Marengo, David L. Farnsworth^*

Affiliation(s)

School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York, USA.

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.

KEYWORDS

Conditional Variance Formula, Conditioning, Geometric Representation, Minimum Variance Estimator, Rao-Blackwell Theorem, Sufficient Statistic, Unbiased Estimator

Share and Cite:

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

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