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Journal article
Uniformly Minimum Variance Unbiased Estimators (UMVUE) Not Attaining Cramer-Rao Lower Bounds
International Journal of Statistical Sciences, Vol.24(20), p.18
12/23/2024
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.
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Details
- Title
- Uniformly Minimum Variance Unbiased Estimators (UMVUE) Not Attaining Cramer-Rao Lower Bounds
- Publication Details
- International Journal of Statistical Sciences, Vol.24(20), p.18
- Resource Type
- Journal article
- Publisher
- Department of Statistics, University of Rajshahi, Bangladesh
- Copyright
- Copyright (c) 2024 Department of Statistics, University of Rajshahi, Rajshahi
- Identifiers
- 99381378976006600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English