Uniformly Minimum Variance Unbiased Estimators (UMVUE) Not Attaining Cramer-Rao Lower Bounds

Authors

  • S C Bagui Department of Mathematics and Statistics, University of West Florida, FL 32514 USA
  • K L Mehra Department of Mathematical and Statistical Sciences, University of Alberta, AB, Canada

DOI:

https://doi.org/10.3329/ijss.v24i20.78210

Keywords:

Ancillary statistics, Complete statistics, Minimal Sufficiency, Unbiased estimator, Rao-Blackwell theorem, Lehmann-Scheffé theorem

Abstract

The main thrust of this article is to provide counterexamples where the variance of the UMVUE does not achieve the Cramer-Rao lower bound. We provided many motivating counterexamples and showed that these UMVU estimators are, in fact, asymptotically efficient estimators. All counterexamples are new or may not be available in standard textbooks. To illustrate the entire process, we supplied many definitions related to UMVUE and described various methods and step-by-step approaches for finding UMVUE’s. In concluding remarks, we also gave a short biography of Professor C.R. Rao. It is hoped that the article will have pedagogical value in courses on statistical inference.

IJSS, Vol. 24(2) Special, December, 2024, pp 1-18

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Published

2024-12-23

How to Cite

Bagui, S. C., & Mehra, K. L. (2024). Uniformly Minimum Variance Unbiased Estimators (UMVUE) Not Attaining Cramer-Rao Lower Bounds. International Journal of Statistical Sciences , 24(20), 1–18. https://doi.org/10.3329/ijss.v24i20.78210

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Section

Original Articles