Geodesic
Large deviations for sums of bounded functions of a normalized sample under gamma distribution
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 166-178
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We study large deviations of a widely used class of scale-free statistics under gamma distribution. We show that the constraints on the functions defining these statistics can be relaxed with respect to the previously obtained result. The result is applied to a recent exponentiality test. 
@article{ZNSL_2015_442_a10,
     author = {A. V. Tchirina},
     title = {Large deviations for sums of bounded functions of a~normalized sample under gamma distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {166--178},
     year = {2015},
     volume = {442},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a10/}
}
TY  - JOUR
AU  - A. V. Tchirina
TI  - Large deviations for sums of bounded functions of a normalized sample under gamma distribution
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 166
EP  - 178
VL  - 442
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a10/
LA  - ru
ID  - ZNSL_2015_442_a10
ER  - 
%0 Journal Article
%A A. V. Tchirina
%T Large deviations for sums of bounded functions of a normalized sample under gamma distribution
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 166-178
%V 442
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a10/
%G ru
%F ZNSL_2015_442_a10
A. V. Tchirina. Large deviations for sums of bounded functions of a normalized sample under gamma distribution. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 166-178. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a10/

[1] R. R. Bahadur, Some Limit Theorem in Statistics, SIAM, Philadelphia, 1971 | MR

[2] L. Baringhaus, F. Taherizade, “A K-S type test for exponentiality based on empirical Hankel transforms”, Comm. Stat. Theor. Meth., 42 (2013), 3781–3792 | DOI | MR | Zbl

[3] H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on sums of observations”, Ann. Math. Statist., 23:4 (1952), 493–507 | DOI | MR | Zbl

[4] Ya. Yu. Nikitin, Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[5] D. Plachky, J. Steinebach, “A theorem about probabilities of large deviations with an application to queuing theory”, Periodica Mathematica Hungarica, 6:4 (1975), 343–345 | DOI | MR | Zbl

[6] A. V. Chirina, “Bolshie ukloneniya nekotorykh svobodnykh ot parametra masshtaba funktsii ot vyborki iz gamma-raspredeleniya”, Zap. nauchn. semin. POMI, 298, 2003, 252–279 | MR | Zbl

[7] Won Qyu Kim, “A non-compact generalization of Horvath's intersection theorem”, Bull. Korean Math. Soc., 32:2 (1995), 153–162 | MR | Zbl