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1.
Andrew L. Rukhin 《Journal of Theoretical Probability》1993,6(1):71-87
The risk influence function is defined as the directional derivative of the risk of the Bayes rule. The properties of this function are studied and the relationship between unimodal prior distribution and the shape of the frequentist risk of the corresponding Bayes procedure is examined. 相似文献
2.
A. A. Mogul’skii 《Siberian Mathematical Journal》2008,49(4):669-683
We obtain an integro-local limit theorem for the sum S(n) = ξ(1)+?+ξ(n) of independent identically distributed random variables with distribution whose right tail varies regularly; i.e., it has the form P(ξ≥t) = t ?β L(t) with β > 2 and some slowly varying function L(t). The theorem describes the asymptotic behavior on the whole positive half-axis of the probabilities P(S(n) ∈ [x, x + Δ)) as x → ∞ for a fixed Δ > 0; i.e., in the domain where the normal approximation applies, in the domain where S(n) is approximated by the distribution of its maximum term, as well as at the “junction” of these two domains. 相似文献