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Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures

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  • معلومة اضافية
    • Contributors:
      Mathématiques et Informatique Appliquées (MIA-Paris); Institut National de la Recherche Agronomique (INRA)-AgroParisTech; CEntre de REcherches en MAthématiques de la DEcision (CEREMADE); Université Paris Dauphine-PSL; Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS); Centre de Recherche en Économie et Statistique (CREST); Ecole Nationale de la Statistique et de l'Analyse de l'Information Bruz (ENSAI)-École polytechnique (X); Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS); Department of Economics; Università degli studi di Verona = University of Verona (UNIVR)
    • بيانات النشر:
      HAL CCSD
      Bernoulli Society for Mathematical Statistics and Probability
    • الموضوع:
      2018
    • Collection:
      GENES (Groupe des Écoles Nationales d'Économie et Statistique): HAL
    • نبذة مختصرة :
      arXiv: 1406.4406v1 ; We provide conditions on the statistical model and the prior probability law to derive contraction rates of posterior distributions corresponding to data-dependent priors in an empirical Bayes approach for selecting prior hyper-parameter values. We aim at giving conditions in the same spirit as those in the seminal article of Ghosal and van der Vaart [23]. We then apply the result to specific statistical settings: density estimation using Dirichlet process mixtures of Gaussian densities with base measure depending on data-driven chosen hyper-parameter values and intensity function estimation of counting processes obeying the Aalen model. In the former setting, we also derive recovery rates for the related inverse problem of density deconvolution. In the latter, a simulation study for inhomogeneous Poisson processes illustrates the results.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/1406.4406; hal-01570308; https://hal.science/hal-01570308; https://hal.science/hal-01570308v2/document; https://hal.science/hal-01570308v2/file/Bernoulli_rev.pdf; ARXIV: 1406.4406; PRODINRA: 397314; WOS: 000408286800008
    • الرقم المعرف:
      10.3150/16-BEJ872
    • الدخول الالكتروني :
      https://hal.science/hal-01570308
      https://hal.science/hal-01570308v2/document
      https://hal.science/hal-01570308v2/file/Bernoulli_rev.pdf
      https://doi.org/10.3150/16-BEJ872
    • Rights:
      http://creativecommons.org/licenses/by-sa/ ; info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.F60C2A2B