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Asymptotic distribution of the conditional regret risk for selecting good exponential populations

Shanti S. GuptaFriedrich Liese — 2000


In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang [10] who proved that the regret risk converges to zero with rate O ( n - λ / 2 ) , 0 < λ 2 . The aim of this paper is to study the asymptotic behavior of the conditional regret risk n . It is shown that n n tends in distribution to a linear combination of independent χ 2 -distributed random variables. As an application we...

L 2 -Singular Dichotomy for Orbital Measures on Complex Groups

S. K. GuptaK. E. Hare — 2010

Bollettino dell'Unione Matematica Italiana

It is known that all continuous orbital measures, μ on a compact, connected, classical simple Lie group G or its Lie algebra satisfy a dichotomy: either μ k L 2 or μ k is purely singular to Haar measure. In this note we prove that the same dichotomy holds for the dual situation, continuous orbital measures on the complex group G C . We also determine the sharp exponent k such that any k -fold convolution product of continuous G -bi-invariant measures on G C is absolute continuous with respect to Haar measure.

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