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Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions

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  • Dalal, S. R.

Abstract

A class of random processes with invariant sample paths, that is, processes which yield (with probability one) probability distributions that are invariant under a given transformation group of interest, are introduced and their properties are studied. These processes, named Dirichlet Invariant processes, are closely related to the Dirichlet processes of Ferguson. These processes can be used as priors for Bayesian analysis of some nonparametric problems. As an application Bayes and Minimax estimates of an arbitrary distribution, symmetric about a known point, are obtained.

Suggested Citation

  • Dalal, S. R., 1979. "Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions," Stochastic Processes and their Applications, Elsevier, vol. 9(1), pages 99-107, August.
    • Handle: RePEc:eee:spapps:v:9:y:1979:i:1:p:99-107
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    Cited by:

    1. Ali Karimnezhad & Mahmoud Zarepour, 2020. "A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 321-346, April.
    2. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    3. Hajime Yamato, 1993. "A pólya urn model with a continuum of colors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 453-458, September.

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