Vol. 9, No. 4, 2016

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Bootstrap techniques for measures of center for three-dimensional rotation data

L. Katie Will and Melissa A. Bingham

Vol. 9 (2016), No. 4, 583–590
Abstract

Bootstrapping is a nonparametric statistical technique that can be used to estimate the sampling distribution of a statistic of interest. This paper focuses on implementation of bootstrapping in a new setting, where the data of interest are 3-dimensional rotations. Two measures of center, the mean rotation and spatial average, are considered, and bootstrap confidence regions for these measures are proposed. The developed techniques are then used in a materials science application, where precision is explored for measurements of crystal orientations obtained via electron backscatter diffraction.

Keywords
bootstrap, 3-D rotations, mean matrix, spatial average
Mathematical Subject Classification 2010
Primary: 62G09, 62P30
Milestones
Received: 31 December 2014
Revised: 26 May 2015
Accepted: 31 July 2015
Published: 6 July 2016

Communicated by Mary C. Meyer
Authors
L. Katie Will
Department of Statistics
Iowa State University
Ames, IA 50011
United States
Melissa A. Bingham
Department of Mathematics and Statistics
University of Wisconsin-La Crosse
1725 State Street
La Crosse, WI 54601
United States