Exponential deficiency of convolutions of densities

DOI10.1051/PS/2010010zbMATH Open1266.60021arXiv0905.2944OpenAlexW2963189899MaRDI QIDQ4921827

Iosif Pinelis

Publication date: 14 May 2013

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Abstract: If a probability density p(x) (xinR^k) is bounded and R(t) := int exp(tell(x)) dx < infty for some linear functional ell and all tin(0,1), then, for each tin(0,1) and all large enough n, the n-fold convolution of the t-tilted density p_t(x) := exp(tell(x)) p(x)/R(t) is bounded. This is a corollary of a general, "non-i.i.d." result, which is also shown to enjoy a certain optimality property. Such results are useful for saddle-point approximations.

Full work available at URL: https://arxiv.org/abs/0905.2944

zbMATH Keywords

convolutionboundednessexponential familiesprobability densitycharacteristic functionsexponential tiltingexponential integrabilitysaddle-point approximationabsolute integrabilitysums of independent random variables/vectors

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05) Large deviations (60F10)

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