ABSTRACT
The paper considers nonparametric empirical Bayes estimation of a distribution function having a Dirichlet process prior D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203493205/efe52689-d7cd-469d-aa36-8f9c2548773d/content/eq2853.tif"/> (α). For the case when the size α(R) is unknown, it is shown that the proposed empirical Bayes estimators are asymptotically optimal with order O(n –1), where n is the number of data at hand for the present estimation problem. Therefore, the results of Korwar and Hollander (1976) and Ghosh, Lahiri and Tiwari (1989), in which α(R) is assumed to be known and a rate of order O(n –1) is achieved, are extended to α(R) unknown case.
