Poisson Compound Decision Problem Revisited

The compound decision problem for a vector of independent Poisson random variables with possibly different means has a half-century-old solution. However, it appears that the classical solution needs smoothing adjustment. We discuss three such adjustments. We also present another approach that first...

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Vydáno v:Journal of the American Statistical Association Ročník 108; číslo 502; s. 741 - 749
Hlavní autoři: Brown, Lawrence D, Greenshtein, Eitan, Ritov, Ya’acov
Médium: Journal Article
Jazyk:angličtina
Vydáno: Alexandria Taylor & Francis Group 01.06.2013
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Témata:
Adjustment
Cross-Validation
data analysis
decision making
Decisions
Effectiveness
Empirical Bayes
equations
NPMLE
Poisson distribution
Random variables
Robbins
Simulation
Statistics
Theory and Methods
ISSN:1537-274X, 0162-1459, 1537-274X
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Shrnutí:The compound decision problem for a vector of independent Poisson random variables with possibly different means has a half-century-old solution. However, it appears that the classical solution needs smoothing adjustment. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem. A simulation study shows the effectiveness of the procedures in improving the performance over that of the classical procedure. A real data example is also provided. The procedures depend on a smoothness parameter that can be selected using a nonstandard cross-validation step, which is of independent interest. Finally, we mention some asymptotic results.
Bibliografie:http://dx.doi.org/10.1080/01621459.2013.771582
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ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2013.771582