Antipodally Symmetric Distributions for Orientation Statistics.

Abstract

The conventional antipodally symmetric Bingham matrix distribution on the Stiefel manifold is generalized. Large sample maximum likelihood estimation and uniformity tests are discussed, and a parametric model for axial orientations (X-shapes) is suggested. A generalization of the Khatri-Mardia matrix distribution is developed to provide a model suitable for hybrids (T-shapes). Beran's results on exponential models for directional data are extended to orientation statistics to provide regression estimators and goodness-of-fit tests as alternatives to maximum likelihood estimation and likelihood ratio tests. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1981
Accession Number
ADA097460

Entities

People

  • Michael J. Prentice

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Asymptotic Normality
  • Asymptotic Series
  • Data Science
  • Directional
  • Estimators
  • Goodness Of Fit Tests
  • Information Science
  • Maximum Likelihood Estimation
  • Military Research
  • Multivariate Analysis
  • Orientation (Direction)
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.