Exact Bootstrap Moments of an L-estimator
Dr. Michael D. Ernst
Department of Statistics
University of Florida
and candidate for the Statistics position
Because many bootstrap problems are analytically intractable, the bootstrap is commonly viewed solely as a resampling technique. We show that for the broad class of statistics that are linear combinations of order statistics (L-estimators) exact analytic expressions for the bootstrap mean and variance can be obtained, eliminating the error due to bootstrap resampling. The expressions follow from direct calculation of the bootstrap mean vector and covariance matrix of the whole set of order statistics. We examine the non-negligible error of the resampling approach for estimating the bootstrap variance using some classical L-estimators such as the trimmed mean and the median on some real data. We also consider exact percentiles and moments of more general functions of order statistics.
Monday, 8 March 1999
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)