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Conjugacy as a Distinctive Feature of the Dirichlet Process

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  • LANCELOT F. JAMES
  • ANTONIO LIJOI
  • IGOR PRÜNSTER

Abstract

Recently the class of normalized random measures with independent increments, which contains the Dirichlet process as a particular case, has been introduced. Here a new technique for deriving moments of these random probability measures is proposed. It is shown that, "a priori", most of the appealing properties featured by the Dirichlet process are preserved. When passing to posterior computations, we obtain a characterization of the Dirichlet process as the only conjugate member of the whole class of normalized random measures with independent increments. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

Suggested Citation

  • Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120.
  • Handle: RePEc:bla:scjsta:v:33:y:2006:i:1:p:105-120
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    References listed on IDEAS

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    1. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, pages 31-48.
    2. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    3. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, pages 1221-1246.
    4. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    5. Ding, Xiaobo & Wang, Qihua, 2011. "Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1193-1207.
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    Citations

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    Cited by:

    1. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, pages 417-433.
    2. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    3. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, pages 816-832.
    4. repec:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0365-8 is not listed on IDEAS
    5. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, pages 686-701.
    6. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    7. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
    8. Stefano Favaro & Antonio Lijoi & Igor Prunster, 2011. "Asymptotics for a Bayesian nonparametric estimator of species richness," Quaderni di Dipartimento 144, University of Pavia, Department of Economics and Quantitative Methods.
    9. Collet, Francesca & Leisen, Fabrizio, 2011. "Free completely random measures," DES - Working Papers. Statistics and Econometrics. WS ws112821, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. El-Dakkak, Omar & Peccati, Giovanni & Prünster, Igor, 2014. "Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 51-64.
    11. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.
    12. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, pages 2288-2301.
    13. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    14. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.

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