Organizer:

Alan Polansky, polansky@math.niu.edu

Speakers

10:30 a.m.
Resampling Methods for Spatial Prediction
Soumendra N. Lahiri, Iowa State University
Keywords: Subsampling, Bootstrap, spatial asymptotic structures

Suppose that Z is a spatially distributed random process and it is observed at a finite number of locations yielding the observations Z(1),..., Z(n). An important problem in this context is the prediction of different functionals of the Z-process from the observations Z(1),...,Z(n). In this talk, we formulate a spatial subsampling method and a spatial bootstrap method for making inference in such prediction problems. We show that the proposed resampling methods yield consistent estimators of the mean square prediction error and other population characteristics of a large class of predictors without any specific model assumptions on the spatial process. The spatial asymptotic structure used here is a mixture of the so-called increasing-domain and infill asymptotic structures and is somewhat nonstandard.

11:00 a.m.
Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap
Arthur Yeh, Department of Applied Statistics and Operations Research, Bowling Green State University
with Kesar Singh
Keywords: Balanced confidence region; Bootstrap; Second-order balancedness; Tukey's depth

We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey's depth. The bootstrap is based on normalized or Studentized statistic formed from an i.i.d. random sample obtained from some unknown distribution in $R^q$. The bootstrap points are deleted based on Tukey's depth until the desired confidence level is reached. The proposed confidence regions are shown to be second-order balanced in the context discussed in Beran (1988). We also study the asymptotic consistency of the Tukey's depth-based bootstrap confidence regions. The applicability of the proposed method is demonstrated in a simulation study.

11:30 a.m.
Exact Bootstrap Moments of an $L$-estimator
Michael Ernst, Department of Statistics, Division of Biostatistics, University of Florida
Alan D. Hutson, University of Florida
Keywords: median, order statistics, trimmed mean

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.