Spring Seminar Series - February 21, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
The
Biased Bootstrap and Selected Applications
Brett Presnell
Department of Statistics
University of Florida
Tuesday, February 21, 2006
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
In
standard applications of the bootstrap a parameter functional of
the population distribution is estimated by the value of the
functional when evaluated at the empirical distribution. The biased
bootstrap modifies this "plug-in rule" by adjusting the empirical
distribution to accommodate conditions expressed in the form of
constraints on other functional parameters. These constraints may
arise naturally from the context of the problem, or from a need to
improve an estimator or procedure. Specific applications include a
nonparametric approach to estimation or hypothesis testing in which
the biased bootstrap enables simulation under the model or under the
null hypothesis, bias reduction, nonparametric estimation of variance
stabilizing functions, constrained density estimation, nonparametric
bootstrap recycling, and robust estimation. In this talk, after
explaining the general ideas, I will focus on applications and
particularly on the use of the biased bootstrap in robust estimation.