## The Annals of Statistics

### Exponential Models for Directional Data

Rudolf Beran

#### 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

http://projecteuclid.org/euclid.aos/1176344838

JSTOR

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

#### 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.