Convolution property and exponential bounds for symmetric monotone densities

Claude Lefèvre; Sergey Utev

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 605-613
  • ISSN: 1292-8100

Abstract

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Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 < k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.

How to cite

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Lefèvre, Claude, and Utev, Sergey. "Convolution property and exponential bounds for symmetric monotone densities." ESAIM: Probability and Statistics 17 (2013): 605-613. <http://eudml.org/doc/273631>.

@article{Lefèvre2013,
abstract = {Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 &lt; k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.},
author = {Lefèvre, Claude, Utev, Sergey},
journal = {ESAIM: Probability and Statistics},
keywords = {multiply monotonicity; symmetric densities; unimodality; Wintner’s theorem; Bernstein’s inequality; convolution; -monotone; moment bounds; large deviations},
language = {eng},
pages = {605-613},
publisher = {EDP-Sciences},
title = {Convolution property and exponential bounds for symmetric monotone densities},
url = {http://eudml.org/doc/273631},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Lefèvre, Claude
AU - Utev, Sergey
TI - Convolution property and exponential bounds for symmetric monotone densities
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 605
EP - 613
AB - Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 &lt; k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
LA - eng
KW - multiply monotonicity; symmetric densities; unimodality; Wintner’s theorem; Bernstein’s inequality; convolution; -monotone; moment bounds; large deviations
UR - http://eudml.org/doc/273631
ER -

References

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