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Estimating a Mixing Distribution on the Sphere Using Predictive Recursion

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  • Vaidehi Dixit

    (North Carolina State University)

  • Ryan Martin

    (North Carolina State University)

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.

Suggested Citation

  • Vaidehi Dixit & Ryan Martin, 2022. "Estimating a Mixing Distribution on the Sphere Using Predictive Recursion," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 596-626, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-021-00275-w
    DOI: 10.1007/s13571-021-00275-w
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