Score matching estimators for directional distributions

2016/04/28 by Kanti V. Mardia, Mardia, Kanti V, John T. Kent +3 · 2 citations
Mathematics · #62F10 (Primary) #62H11 (Secondary) #Advanced Statistical Methods and Models #FOS: Mathematics #Morphological variations and asymmetry #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1604.08470

openalex publication_date 2016/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on a compact oriented Riemannian manifold. Important applications include von Mises-Fisher, Bingham and joint models on the sphere and related spaces. The estimator is consistent and asymptotically normally distributed under mild regularity conditions. Further, it is easy to compute as a solution of a linear set of equations and requires no knowledge of the normalizing constant. Several examples are given, both analytic and numerical, to demonstrate its good performance.

Citations

• Probabilistic model for two dependent circular variables

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