# Exponential deficiency of convolutions of densities∗

ESAIM: Probability and Statistics (2012)

- Volume: 16, page 86-96
- ISSN: 1292-8100

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topPinelis, Iosif. "Exponential deficiency of convolutions of densities∗." ESAIM: Probability and Statistics 16 (2012): 86-96. <http://eudml.org/doc/222476>.

@article{Pinelis2012,

abstract = {If a probability density p(x) (x ∈ ℝk) is bounded and
R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density \hbox\{$\tilde p_t$\}
:= e〈x, tu〉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 and their corollaries stated in terms of the absolute integrability of the corresponding characteristic functions are useful for saddle-point approximations. },

author = {Pinelis, Iosif},

journal = {ESAIM: Probability and Statistics},

keywords = {Probability density; saddle-point approximation; sums of independent random variables/vectors; convolution; exponential integrability; boundedness; exponential tilting; exponential families; absolute integrability; characteristic functions; probability density},

language = {eng},

month = {7},

pages = {86-96},

publisher = {EDP Sciences},

title = {Exponential deficiency of convolutions of densities∗},

url = {http://eudml.org/doc/222476},

volume = {16},

year = {2012},

}

TY - JOUR

AU - Pinelis, Iosif

TI - Exponential deficiency of convolutions of densities∗

JO - ESAIM: Probability and Statistics

DA - 2012/7//

PB - EDP Sciences

VL - 16

SP - 86

EP - 96

AB - If a probability density p(x) (x ∈ ℝk) is bounded and
R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density \hbox{$\tilde p_t$}
:= e〈x, tu〉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 and their corollaries stated in terms of the absolute integrability of the corresponding characteristic functions are useful for saddle-point approximations.

LA - eng

KW - Probability density; saddle-point approximation; sums of independent random variables/vectors; convolution; exponential integrability; boundedness; exponential tilting; exponential families; absolute integrability; characteristic functions; probability density

UR - http://eudml.org/doc/222476

ER -

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