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Asymptotic properties of parallel Bayesian kernel density estimators

Author

Listed:
  • Alexey Miroshnikov

    (University of California)

  • Evgeny Savelev

    (Virginia Polytechnic Institute and State University)

Abstract

In this article, we perform an asymptotic analysis of Bayesian parallel kernel density estimators introduced by Neiswanger et al. (in: Proceedings of the thirtieth conference on uncertainty in artificial intelligence, AUAI Press, pp 623–632, 2014). We derive the asymptotic expansion of the mean integrated squared error for the full data posterior estimator and investigate the properties of asymptotically optimal bandwidth parameters. Our analysis demonstrates that partitioning data into subsets requires a non-trivial choice of bandwidth parameters that optimizes the estimation error.

Suggested Citation

  • Alexey Miroshnikov & Evgeny Savelev, 2019. "Asymptotic properties of parallel Bayesian kernel density estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 771-810, August.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:4:d:10.1007_s10463-018-0662-0
    DOI: 10.1007/s10463-018-0662-0
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    References listed on IDEAS

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    1. Tarn Duong & Martin L. Hazelton, 2005. "Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506, September.
    2. de Valpine P., 2004. "Monte Carlo State-Space Likelihoods by Weighted Posterior Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 523-536, January.
    3. M. Sköld & G. O. Roberts, 2003. "Density Estimation for the Metropolis–Hastings Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 699-718, December.
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