Abstract #300097

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JSM 2003 Abstract #300097
Activity Number: 244
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #300097
Title: Rates of Convergence under Modified Bootstrapping
Author(s): Noel D. Veraverbeke*+
Companies: Limburgs University Centrum
Address: Universitaire Campus, B 3590 Diepenbeek, , , Belgium
Keywords: bootstrap ; consistency ; quantiles
Abstract:

The modified or "m out of n" bootstrap uses a resample size m which is different from the original sample size n. It has been shown that this modified bootstrap procedure works consistently in cases where Efron's classical ("n out of n") bootstrap fails. We give new results on the usefulness of the procedure by showing that the modified bootstrap provides faster rates of consistency in situations where the classical bootstrap works. For the class of U-quantiles, we obtain an improved rate of convergence under appropriate choice of m. U-quantiles are generalizations of the usual quantiles, that are taken from the distribution fuction of a symmetric function of several variables. A similar improvement is found for quantiles of the Kaplan-Meier estimator in the model of random right censorship for survival data. Finally we also show how the modified bootstrap works in the case of regression quantiles in a fixed design heteroscedastic regression model.

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