• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Adaptive Bayesian Density Estimation with Location-Scale Mixtures

Kruijer, Willem; Rousseau, Judith; Van Der Vaart, Aad (2009-05), Adaptive Bayesian Density Estimation with Location-Scale Mixtures, 7th Workshop on Bayesian Nonparametrics, 2009-06, Moncalieri, Italie

Type
Communication / Conférence
External document link
http://hal.archives-ouvertes.fr/hal-00389343/en/
Date
2009-05
Conference title
7th Workshop on Bayesian Nonparametrics
Conference date
2009-06
Conference city
Moncalieri
Conference country
Italie
Metadata
Show full item record
Author(s)
Kruijer, Willem
Rousseau, Judith
Van Der Vaart, Aad
Abstract (EN)
We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of a kernel $C_p \exp\{-|x|^p\}$. We construct a finite mixture approximation of densities whose logarithm is locally $\beta$-H\"older, with squared integrable H\"older constant. Under additional tail and moment conditions, the approximation is minimax for both the supremum-norm and the Kullback-Leibler divergence. We use this approximation to establish convergence rates for a Bayesian mixture model with priors on the weights, locations, and the number of components. Regarding these priors, we provide general conditions under which the posterior converges at a near optimal rate, and is rate-adaptive with respect to the smoothness of $\log f_0$. Examples of priors which satisfy these conditions include Dirichlet and Polya-tree priors for the weights, and Poisson processes for the locations.
Subjects / Keywords
Rate-adaptive density estimation; Bayesian density estimation; Nonparametric density estimation; Convergence Rates; Location-Scale Mixtures

Related items

Showing items related by title and author.

  • Thumbnail
    Adaptive Bayesian Estimation of a spectral density 
    Rousseau, Judith; Kruijer, Willem (2011) Document de travail / Working paper
  • Thumbnail
    Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors 
    Rousseau, Judith; Kruijer, Willem (2013) Article accepté pour publication ou publié
  • Thumbnail
    On Bayesian Estimation of the Long-Memory Parameter in the FEXP-Model for Gaussian Time Series 
    Kruijer, Willem; Rousseau, Judith (2010) Communication / Conférence
  • Thumbnail
    Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density 
    Rousseau, Judith (2010) Article accepté pour publication ou publié
  • Thumbnail
    Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density 
    Rousseau, Judith (2009) Communication / Conférence
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo