Statistical Science

Developments in Decision-Theoretic Variance Estimation

Jon M. Maatta and George Casella

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Abstract

This article traces the history of the problem of estimating the variance, $\sigma^2$, based on a random sample from a normal distribution with mean $\mu$ unknown. Considered are both the point estimation and confidence interval cases. We see that improvement over both usual estimators follows a remarkably parallel development and stemmed from the innovative ideas presented in Stein (1964). We examine developments through the most recent dealing with improved confidence intervals and conditional evaluations of interval estimators.

Article information

Source
Statist. Sci., Volume 5, Number 1 (1990), 90-101.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177012263

Digital Object Identifier
doi:10.1214/ss/1177012263

Mathematical Reviews number (MathSciNet)
MR1054858

Zentralblatt MATH identifier
0955.62529

JSTOR
links.jstor.org

Keywords
Point estimation confidence intervals conditional confidence invariance

Citation

Maatta, Jon M.; Casella, George. Developments in Decision-Theoretic Variance Estimation. Statist. Sci. 5 (1990), no. 1, 90--101. doi:10.1214/ss/1177012263. https://projecteuclid.org/euclid.ss/1177012263


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See also

  • See Comment: James O. Berger. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 102--103.
  • See Comment: Lawrence D. Brown. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 103--106.
  • See Comment: Arthur Cohen. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 106--107.
  • See Comment: Edward I. George. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 107--109.
  • See Comment: Jiunn T. Hwang. [Developments in Decision-Theoretic Variance Estimation]: Comment: How Much Can the Improvements be Realized?. Statist. Sci., Volume 5, Number 1 (1990), 110--111.
  • See Comment: K. Brenda MacGibbon, Glenn E. Shorrock. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 112--113.
  • See Comment: Andrew L. Rukhin. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 113--116.
  • See Comment: William E. Strawderman. [Developments in Decision-Theoretic Variance Estimation]: Comment. Statist. Sci., Volume 5, Number 1 (1990), 117--118.
  • See Comment: Jon M. Maatta, George Casella. [Developments in Decision-Theoretic Variance Estimation]: Rejoinder. Statist. Sci., Volume 5, Number 1 (1990), 118--120.