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Point Estimation of the Central Orientation of Random Rotations

Summary: [This abstract is based on the authors' abstract.] Data as three-dimensional rotations have application in computer science, kinematics, and materials sciences, among other areas. Estimating the central orientation from a sample of such data is an important problem, which is complicated by the fact that several different approaches exist for this, motivated by various geometrical and decision-theoretical considerations. However, little is known about how such estimators compare, especially on common distributions for location models with random rotations. The authors examine four location estimators, three of which are commonly found in different literatures; the fourth estimator (a projected median) is newly introduced. This study unifies existing literature and provides a detailed numerical investigation of location estimators for three commonly used rotation distributions in statistics and materials science. While the data-generating model influences the best choice of an estimator, the proposed projected median emerges as an overall good performer, which can be suggested without particular distributional assumptions. The authors illustrate the estimators and their findings with data from a materials science study by approximating the central orientation of cubic crystals on the microsurface of a metal. Accompanying supplementary materials are available online.

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  • Topics: Statistics
  • Keywords: Process dynamics, Location, Estimation, Median, Geometric distribution
  • Author: Stanfill, Bryan; Genschel, Ulrike; Hofmann, Heike;
  • Journal: Technometrics