Exponential deficiency of convolutions of densities

Iosif Pinelis

doi:10.1051/ps/2010010

All issues

Volume 16 (2012)

ESAIM: PS, 16 (2012) 86-96

References

Free Access

Issue		ESAIM: PS Volume 16, 2012


Page(s)		86 - 96
DOI		https://doi.org/10.1051/ps/2010010
Published online		02 July 2012

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R.N. Bhattacharya and R.R. Rao, Normal approximation and asymptotic expansions. Robert E. Krieger Publishing Co. Inc., Melbourne, FL (1986). Reprint of the 1976 original. [Google Scholar]
H.E. Daniels, Tail probability approximations. Int. Stat. Rev. 55 (1987) 37–48. [CrossRef] [Google Scholar]
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B.-Y. Jing, Q.-M. Shao and W. Zhou, Saddlepoint approximation for Student’s t-statistic with no moment conditions. Ann. Stat. 32 (2004) 2679–2711. [CrossRef] [MathSciNet] [Google Scholar]
C. Klüppelberg, Subexponential distributions and characterizations of related classes. Probab. Theory Relat. Fields 82 (1989) 259–269. [CrossRef] [Google Scholar]
R. Lugannani and S. Rice, Saddle point approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab. 12 (1980) 475–490. [CrossRef] [Google Scholar]
I.F. Pinelis, Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables, in Limit theorems of probability theory. “Nauka” Sibirsk. Otdel., Novosibirsk. Trudy Inst. Mat. 5 (1985) 144–173, 176. [Google Scholar]
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Q.-M. Shao, Recent progress on self-normalized limit theorems, in Probability, finance and insurance. World Sci. Publ., River Edge, NJ (2004) 50–68. [Google Scholar]

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[1] O. Barndorff-Nielsen and D.R. Cox, Edgeworth and saddle-point approximations with statistical applications. J. R. Stat. Soc., Ser. B 41 (1979) 279–312. With discussion. [Google Scholar]

[2] R.N. Bhattacharya and R.R. Rao, Normal approximation and asymptotic expansions. Robert E. Krieger Publishing Co. Inc., Melbourne, FL (1986). Reprint of the 1976 original. [Google Scholar]

[3] H.E. Daniels, Tail probability approximations. Int. Stat. Rev. 55 (1987) 37–48. [CrossRef] [Google Scholar]

[4] P. Embrechts and C.M. Goldie, On convolution tails. Stoch. Proc. Appl. 13 (1982) 263–278. [CrossRef] [Google Scholar]

[5] B.-Y. Jing, Q.-M. Shao and W. Zhou, Saddlepoint approximation for Student’s t-statistic with no moment conditions. Ann. Stat. 32 (2004) 2679–2711. [CrossRef] [MathSciNet] [Google Scholar]

[6] C. Klüppelberg, Subexponential distributions and characterizations of related classes. Probab. Theory Relat. Fields 82 (1989) 259–269. [CrossRef] [Google Scholar]

[7] R. Lugannani and S. Rice, Saddle point approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab. 12 (1980) 475–490. [CrossRef] [Google Scholar]

[8] I.F. Pinelis, Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables, in Limit theorems of probability theory. “Nauka” Sibirsk. Otdel., Novosibirsk. Trudy Inst. Mat. 5 (1985) 144–173, 176. [Google Scholar]

[9] N. Reid, Saddlepoint methods and statistical inference. Stat. Sci. 3 (1988) 213–238. With comments and a rejoinder by the author. [CrossRef] [Google Scholar]

[10] Q.-M. Shao, Recent progress on self-normalized limit theorems, in Probability, finance and insurance. World Sci. Publ., River Edge, NJ (2004) 50–68. [Google Scholar]