Bounds for robust maximum likelihood and posterior consistency in compound mixture state experiments

Suman Majumdar, Dennis Gilliland and James Hannan

Statistics & Probability Letters, 1999, vol. 41, issue 3, 215-227

Abstract: Uniform bounds on rates of L1-consistency for the empiric mean of state sequences in a family of probability models (compound with finite-mixture-state component) are obtained for MLEs (Section sec2) and posterior means for quasi-uniform hyperpriors (Section sec3), both determined in the iid mixture (empirical Bayes) sub-models. Qualitative aspects of results of this type were described by Robbins (1951). Application to the Gilliland and Hannan (1974/86) restricted-risk-finite-state-component compound decision problem (Section sec4) yields uniform bounds on rates of asymptotic regret of Bayes solutions therein (with extension to mixture-state by expectation), giving strong affirmation to an asymptotic form of a Robbins (1951) conjecture. The general extension to mixture-state components (Remark rem4.1) strengthens much of the existing compound literature.

Keywords: Asymptotic; regret; Compound; Consistency; Maximum; likelihood; Posterior (search for similar items in EconPapers)
Date: 1999
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