On constructing sequences estimating the mixing distribution with applications
作者:
Robert F. Phillips,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1990)
卷期:
Volume 19,
issue 2
页码: 705-720
ISSN:0361-0918
年代: 1990
DOI:10.1080/03610919008812883
出版商: Marcel Dekker, Inc.
关键词: mixture;Chebychev norm;linear programming;nonparametric empirical Bayes;density estimate
数据来源: Taylor
摘要:
This paper shows that by minimizing a Chebychev norm a mixing distribution can be constructed which converges weakly to the true mixing distribution with probability one. Deely and Kruse (1968) established a similar result for the supremum norm. For both norms the constructed mixing distribution is computed by solving a linear programming problem, but this problem is considerably smaller when the Chebychev norm is used. Thus a suitable mixing distribution can be constructed from solving a linear programming problem with considerably less computational work than was previously known. To illustrate the application of this simpler procedure it is applied to derive nonparametric empirical Bayes estimates in a simulation study. Some density estimates are also illustrated.
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