Work

Stein’s method of moments on the sphere

Year: 2026

Type: article

Abstract: We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads to explicit estimators which have good asymptotic properties (close to efficiency) and therefore provide interesting alternatives to classical maximum likelihood methods or more recent score matching estimators. We perform competitive simulation studies to assess the quality of the new estimators. Finally, the practical relevance of our estimators is illustrated on a real data application in spherical latent representations of handwritten numbers.

Source: Bernoulli

DOI: 10.3150/25-bej1898

Authors: Adrian Fischer, Robert E. Gaunt, Yvik Swan

Institutions: University of Oxford, University of Manchester, Université Libre de Bruxelles

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds De La Recherche Scientifique - FNRS, Engineering and Physical Sciences Research Council

Awards: Rates of Convergence in Multivariate Normal Approximation by Stein's Method, CHARMNET - Characterising Models for Networks