The Annals of Statistics

Estimating Events

Michael Evans

Full-text: Open access

Abstract

The problem of estimating an event, having positive probability content, based on a sample of $n$ observations is considered. A natural metric is shown to exist on the space of possible values for the event. This leads to the definition of optimal estimators. We derive optimal estimators for events which correspond to quantiles for the univariate exponential model. Further optimal estimators are derived for the events bounded by the ellipsoidal contours of the density function in the multivariate normal model.

Article information

Source
Ann. Statist., Volume 11, Number 4 (1983), 1218-1224.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346334

Digital Object Identifier
doi:10.1214/aos/1176346334

Mathematical Reviews number (MathSciNet)
MR720266

Zentralblatt MATH identifier
0542.62041

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62H99: None of the above, but in this section 62C99: None of the above, but in this section

Keywords
Random set estimators equivariance univariate exponential multivariate normal

Citation

Evans, Michael. Estimating Events. Ann. Statist. 11 (1983), no. 4, 1218--1224. doi:10.1214/aos/1176346334. https://projecteuclid.org/euclid.aos/1176346334


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