An empirical bayes two action problem with nonidentical components for a translated exponential distribution
- 1 January 1975
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics
- Vol. 4 (8) , 767-775
- https://doi.org/10.1080/03610927308827286
Abstract
Let θ be a one dimensional random variable with distribution G with support in (0,∞) and let an observation be taken from a population with density is a known constant. A decision is to be made between where c is a known constant with loss function . Given that the preceding problem occurs repeatedly and independently with G unknown and K varying in from problem to problem, an empirical Bayes procedure is exhibited whose expected risk less a minimum Bayes risk is 0(n −θ;/4) whenever . The procedure depends on the estimation of a marginal density h and a weighted integral of h using the inversion formula for some absolutely integrable characteristic functions. Extension of these results to the case of a two-dimensional random vector (θ1, δ2) is also discussed.Keywords
This publication has 3 references indexed in Scilit:
- Convergence Rates for Empirical Bayes Two-Action Problems II. Continuous CaseThe Annals of Mathematical Statistics, 1972
- The Empirical Bayes Approach to Statistical Decision ProblemsThe Annals of Mathematical Statistics, 1964
- The Empirical Bayes Approach to Testing Statistical HypothesesRevue de l'Institut International de Statistique / Review of the International Statistical Institute, 1963