Bootstrapping a Universal Pivot When Nuisance Parameters are Estimated

John E. Angus

The American Statistician, 2016, vol. 70, issue 1, 100-107

Abstract: In complete samples from a continuous cumulative distribution with unknown parameters, it is known that various pivotal functions can be constructed by appealing to the probability integral transform. A pivotal function (or simply pivot) is a function of the data and parameters that has the property that its distribution is free of any unknown parameters. Pivotal functions play a key role in constructing confidence intervals and hypothesis tests. If there are nuisance parameters in addition to a parameter of interest, and consistent estimators of the nuisance parameters are available, then substituting them into the pivot can preserve the pivot property while altering the pivot distribution, or may instead create a function that is approximately a pivot in the sense that its asymptotic distribution is free of unknown parameters. In this latter case, bootstrapping has been shown to be an effective way of estimating its distribution accurately and constructing confidence intervals that have more accurate coverage probability in finite samples than those based on the asymptotic pivot distribution. In this article, one particular pivotal function based on the probability integral transform is considered when nuisance parameters are estimated, and the estimation of its distribution using parametric bootstrapping is examined. Applications to finding confidence intervals are emphasized. This material should be of interest to instructors of upper division and beginning graduate courses in mathematical statistics who wish to integrate bootstrapping into their lessons on interval estimation and the use of pivotal functions.[Received November 2014. Revised August 2015.]

Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2015.1086436 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:amstat:v:70:y:2016:i:1:p:100-107

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20

DOI: 10.1080/00031305.2015.1086436

Access Statistics for this article

The American Statistician is currently edited by Eric Sampson

More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().