The Generalized Bootstrap: A New Fitting Strategy and Simulation Study Showing Advantage over Bootstrap Percentile Methods

Authored by: Weixing Cai , Edward J. Dudewicz

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-27

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Abstract

Chernick (1999, pp. 54–55) notes that Efron and Tibshirani (1993) describe four methods for constructing approximate confidence intervals for a parameter. One of these methods, in fact perhaps the most popular method and the method covered in such excellent introductory works as that of Moore and McCabe (2003), is the bootstrap percentile method. The generalized bootstrap (GB) was introduced formally in Dudewicz (1992). It has as its essence fitting a suitable distribution to the available data, and then taking samples from the fitted distribution. The fitted GLD implementation of the GB chooses to fit a distribution F with an F? from the Generalized Lambda Distribution family. Karian and Dudewicz (2000) introduce three methods of fitting as the GB. We combine these methods, which we describe with corresponding algorithms, into a fitting strategy. This strategy is then used in a simulation study. Through the simulation study, we show that the GB has an advantage over the bootstrap for the goal of covering the true value of the upper limit of a uniform distribution with empirical confidence intervals.

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