Convolution property and exponential bounds for symmetric monotone densities
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 605-613

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.

DOI : 10.1051/ps/2012012
Classification : 60E10, 60E15
Keywords: multiply monotonicity, symmetric densities, unimodality, Wintner's theorem, Bernstein's inequality 
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     author = {Lef\`evre, Claude and Utev, Sergey},
     title = {Convolution property and exponential bounds for symmetric monotone densities},
     journal = {ESAIM: Probability and Statistics},
     pages = {605--613},
     year = {2013},
     publisher = {EDP Sciences},
     volume = {17},
     doi = {10.1051/ps/2012012},
     mrnumber = {3085635},
     zbl = {1291.60030},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2012012/}
}
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Lefèvre, Claude; Utev, Sergey. Convolution property and exponential bounds for symmetric monotone densities. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 605-613. doi: 10.1051/ps/2012012

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