Skip to main content

Estimation of the Central Orientation for Rotation Data

Jan 10, 2014 - 10:00 AM
to , -

Estimation of the Central Orientation for Rotation Data

 

Date: Friday, January 10
Time: 10:00 am -- 10:50 am
Place: Snedecor 2113
Speaker: Bryan Stanfill, Department of Statistics, Iowa State University, Ames

Abstract:

Three-dimensional orientation data, with observations as 3-by-3 rotation matrices, have applications in many areas such as computer science, kinematics and materials sciences. Estimating the central orientation parameter S from a sample of such data is an important problem, which is complicated by the fact that several different approaches exist where each is motivated by various geometrical and decision-theoretic considerations.  Little is known about how such estimators compare, however, especially on common distributions for location models with random rotations.  We closely examine the performance of the following two estimators: the projected arithmetic mean which is well known and has been shown to perform favorably when the data are sufficiently concentrated and a newly introduced estimator called the projected median.  Specifically, we discuss asymptotic properties of the projected median including the estimator's limiting distribution and propose two nonparametric methods to set confidence regions for the central orientation parameter S based on this median estimator.  We further show that unlike the projected arithmetic mean, this median estimator is SB-robust and lends itself to an alternative estimator when data come from heavy-tailed distributions or data contamination presents an issue. We illustrate our results through a simulation study.