Abstract
For a vast class of discrete model families where the natural parameter is constrained to an interval, we give conditions for which the Bayes estimator with respect to a boundary supported prior is minimax under squared error loss type functions. Building on a general development of Éric Marchand and Ahmad Parsian, applicable to squared error loss, we obtain extensions to various parametric functions and squared error loss type functions. We provide illustrations for various distributions and parametric functions, and these include examples for many common discrete distributions, as well as when the parametric function is a zero-count probability, an odds-ratio, a Binomial variance, and a Negative Binomial variance, among others.
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The Research of M. Jafari Jozani is supported by a grant of the Institute for Research and Planning in Higher Education, Ministry of Science, Research and Technology, Iran. The Research of É. Marchand is supported by NSERC of Canada.
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Jozani, M.J., Marchand, É. Minimax estimation of constrained parametric functions for discrete families of distributions. Metrika 66, 151–160 (2007). https://doi.org/10.1007/s00184-006-0102-7
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DOI: https://doi.org/10.1007/s00184-006-0102-7