Estimating a Mixing Distribution on the Sphere Using Predictive Recursion

Vaidehi Dixit () and Ryan Martin ()
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Vaidehi Dixit: North Carolina State University
Ryan Martin: North Carolina State University

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 7, 596-626

Abstract: Abstract Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a common problem for data taking values in a Euclidean space, but the work on mixing distribution estimation based on directional data taking values on the unit sphere is limited. In this paper, we propose using the predictive recursion (PR) algorithm to solve for a mixture on a sphere. One key feature of PR is its computational efficiency. Moreover, compared to likelihood-based methods that only support finite mixing distribution estimates, PR is able to estimate a smooth mixing density. PR’s asymptotic consistency in spherical mixture models is established, and simulation results showcase its benefits compared to existing likelihood-based methods. Using PR we propose a method for goodness-of-fit testing and a clustering mechanism in the context of directional data with two real-data illustrations.

Keywords: Directional data; EM algorithm; Marginal likelihood; Mixture model; Von Mises–Fisher distribution.; Primary 62G07; Secondary 62G10, 62G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-021-00275-w

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