The Annals of Statistics

Exponential Models for Directional Data

Rudolf Beran

Full-text: Open access

Abstract

A rotationally invariant exponential model, which includes the Fisher-von Mises and Bingham distributions as special cases, is proposed for directional data in $R^p(p \geqslant 2)$. A new regression estimator for the model parameters is developed as a competitor to the maximum likelihood estimator. Both the new estimator and the MLE are asymptotically efficient at the postulated model and are robust under small departures from that model. Computationally, the regression estimator is much simpler since it requires no iterations or numerical integrations. Goodness-of-fit can be assessed by fitting nested special cases of the general model to the data.

Article information

Source
Ann. Statist. Volume 7, Number 6 (1979), 1162-1178.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176344838

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176344838

Mathematical Reviews number (MathSciNet)
MR550142

Zentralblatt MATH identifier
0426.62030

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62F10: Point estimation

Keywords
Directional data axial data rotational invariance exponential family asymptotically efficient estimator robust estimator density estimator goodness-of-fit tests

Citation

Beran, Rudolf. Exponential Models for Directional Data. Ann. Statist. 7 (1979), no. 6, 1162--1178. doi:10.1214/aos/1176344838. http://projecteuclid.org/euclid.aos/1176344838.


Export citation