IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v71y2019i4d10.1007_s10463-018-0662-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-018-0662-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-018-0662-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    2. Billings, Stephen B. & Johnson, Erik B., 2012. "A non-parametric test for industrial specialization," Journal of Urban Economics, Elsevier, vol. 71(3), pages 312-331.
    3. Boris Branisa & Adriana Cardozo, 2009. "Regional Growth Convergence in Colombia Using Social Indicators," Ibero America Institute for Econ. Research (IAI) Discussion Papers 195, Ibero-America Institute for Economic Research.
    4. Bertl Johanna & Ewing Gregory & Kosiol Carolin & Futschik Andreas, 2017. "Approximate maximum likelihood estimation for population genetic inference," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(5-6), pages 387-405, December.
    5. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    6. Seppo Pulkkinen & Marko Mäkelä & Napsu Karmitsa, 2013. "A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates," Journal of Global Optimization, Springer, vol. 56(2), pages 459-487, June.
    7. Fabian Krüger & Sebastian Lerch & Thordis Thorarinsdottir & Tilmann Gneiting, 2021. "Predictive Inference Based on Markov Chain Monte Carlo Output," International Statistical Review, International Statistical Institute, vol. 89(2), pages 274-301, August.
    8. Boris Branisa & Adriana Cardozo, 2009. "Revisiting the Regional Growth Convergence Debate in Colombia Using Income Indicators," Ibero America Institute for Econ. Research (IAI) Discussion Papers 194, Ibero-America Institute for Economic Research, revised 21 Aug 2009.
    9. Tao Hu & Xinyan Zhu & Lian Duan & Wei Guo, 2018. "Urban crime prediction based on spatio-temporal Bayesian model," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-18, October.
    10. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
    11. Adjemian, Stéphane & Bastani, Houtan & Juillard, Michel & Karamé, Fréderic & Mihoubi, Ferhat & Mutschler, Willi & Pfeifer, Johannes & Ratto, Marco & Rion, Normann & Villemot, Sébastien, 2022. "Dynare: Reference Manual Version 5," Dynare Working Papers 72, CEPREMAP, revised Mar 2023.
      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," PSE Working Papers hal-04219920, HAL.
      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," Working Papers hal-04219920, HAL.
    12. Yan, Hanhuan & Han, Liyan, 2019. "Empirical distributions of stock returns: Mixed normal or kernel density?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 473-486.
    13. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    14. Sigve Hovda, 2014. "Using pseudometrics in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 669-696, December.
    15. Rutger Jan Lange, 2020. "Bellman filtering for state-space models," Tinbergen Institute Discussion Papers 20-052/III, Tinbergen Institute, revised 19 May 2021.
    16. Simone Giannerini & Greta Goracci, 2023. "Entropy-Based Tests for Complex Dependence in Economic and Financial Time Series with the R Package tseriesEntropy," Mathematics, MDPI, vol. 11(3), pages 1-27, February.
    17. Gimenez, Olivier & Rossi, Vivien & Choquet, Rémi & Dehais, Camille & Doris, Blaise & Varella, Hubert & Vila, Jean-Pierre & Pradel, Roger, 2007. "State-space modelling of data on marked individuals," Ecological Modelling, Elsevier, vol. 206(3), pages 431-438.
    18. Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
    19. Mathieu Langlard & Fabrice Lamadie & Sophie Charton & Johan Debayle, 2021. "Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 549-567, June.
    20. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:71:y:2019:i:4:d:10.1007_s10463-018-0662-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.