On constructing sequences estimating the mixing distribution with applications |
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Authors: | Robert F Phillips |
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Institution: | Department of Economics , The George Washington University , Washington, DC 20052 |
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Abstract: | 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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Keywords: | mixture Chebychev norm linear programming nonparametric empirical Bayes density estimate |
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