JSM 2004 - Toronto

Abstract #300191

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Activity Number: 362
Type: Invited
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract - #300191
Title: Graphical Diagnostics for the Bootstrap
Author(s): Angelo J. Canty*+
Companies: McMaster University
Address: 218 Hamilton Hall, Hamilton, ON, L8S 4K1, Canada
Keywords: bootstrap ; diagnostics ; graphics ; discreteness ; inconsistency ; pivot
Abstract:

Over the past 25 years the bootstrap has become one of the most widely used tools for many applied statisticians. Like any statistical method, the bootstrap is based on various assumptions and when these assumptions are violated the results of a bootstrap can be very misleading. In many applications of the bootstrap, however, the underlying assumptions are never tested. One of the reasons for this has been the lack of any useful diagnostic tools to assist the applied statistician in checking the assumptions. I will describe some simple graphical diagnostics that can be used to look for potential problems with the bootstrap and suggest remedies where possible. Among the problems that I shall consider are: discreteness of the bootstrap distribution, the effect of outliers, and inconsistency of the bootstrap method. Another topic that I shall examine is the choice of scale that makes a bootstrap statistic approximately pivotal and so stabilizes confidence interval calculations.

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