The Annals of Statistics

On a Class of Bayesian Nonparametric Estimates: I. Density Estimates

Albert Y. Lo

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Given a positive, normalized kernel and a finite measure on an Euclidean space, we construct a random density by convoluting the kernel with the Dirichlet random probability indexed by the finite measure. The posterior distribution of the random density given a sample is classified. The Bayes estimator of the density function is given.

Article information

Ann. Statist. Volume 12, Number 1 (1984), 351-357.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Zentralblatt MATH identifier


Primary: 62A15
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62G05: Estimation

Decision theory Bayesian nonparametric method density estimation


Lo, Albert Y. On a Class of Bayesian Nonparametric Estimates: I. Density Estimates. Ann. Statist. 12 (1984), no. 1, 351--357. doi:10.1214/aos/1176346412.

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See also

  • Part II: Albert Y. Lo, Chung-Sing Weng. On a Class of Bayesian Nonparametric Estimates: II: Hazard Rate Estimates. Ann. Inst. Statist. Math., vol. 41, no. 2, 227--245.