Bolthausen, E (1987). Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima. Probability Theory and Related Fields, 76(2):167-206.
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We consider expressions of the form Z n =E(exp nF(S n /n)) where S n is the sum of n i.i.d. random vectors with values in a Banach space and F is a smooth real valued function. By results of Donsker-Varadhan and Bahadur-Zabell one knows that lim (1/n) log Z n =sup x F(x)-h(x) where h is the so-called entropy function. In an earlier paper a more precise evaluation of Z n is given in the case where there was a unique point maximizing F-h and the curvature at the maximum was nonvanishing. The present paper treats the more delicate problem where these conditions fail to hold.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||Laplace approximations; degenerate maxima; manifolds of maxima; entropy function|
|Deposited On:||20 Oct 2009 13:56|
|Last Modified:||05 Apr 2016 13:29|
|Additional Information:||The original publication is available at www.springerlink.com|
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