Geodesic
On asymptotic efficiency of exponentiality tests based on Rossberg's characterization
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 95-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We construct new tests of exponentiality based on Rossberg's characterization of exponential law. We compute limiting distributions of new tests, local Bahadur efficiency for common alternatives and describe conditions of their local asymptotic optimality. Bibl. – 13 titles. 
@article{ZNSL_2009_368_a6,
     author = {K. Yu. Volkova},
     title = {On asymptotic efficiency of exponentiality tests based on {Rossberg's} characterization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--109},
     year = {2009},
     volume = {368},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a6/}
}
TY  - JOUR
AU  - K. Yu. Volkova
TI  - On asymptotic efficiency of exponentiality tests based on Rossberg's characterization
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 95
EP  - 109
VL  - 368
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a6/
LA  - ru
ID  - ZNSL_2009_368_a6
ER  - 
%0 Journal Article
%A K. Yu. Volkova
%T On asymptotic efficiency of exponentiality tests based on Rossberg's characterization
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 95-109
%V 368
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a6/
%G ru
%F ZNSL_2009_368_a6
K. Yu. Volkova. On asymptotic efficiency of exponentiality tests based on Rossberg's characterization. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 95-109. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a6/

[1] V. S. Korolyuk, Yu. V. Borovskikh, Teoriya $U$-statistik, Naukova Dumka, Kiev, 1989 | MR | Zbl

[2] V. V. Litvinova, Asimptoticheskie svoistva kriteriev simmetrii i soglasiya, osnovannykh na kharakterizatsiyakh, Kandidatskaya dissertatsiya, SPbGU, 2004

[3] Ya. Yu. Nikitin, Asimptoticheskaya effektivnost neparametricheskikh statisticheskikh kriteriev, Nauka, M., 1995 | MR

[4] Ya. Yu. Nikitin, E. V. Ponikarov, “Grubaya asimptotika veroyatnostei bolshikh uklonenii chernovskogo tipa dlya funktsionalov Mizesa”, Tr. S.-Peterb. matem. obschestva, 7, 1999, 124–167 | MR

[5] A. V. Chirina, Asimptoticheskaya effektivnost kriteriev eksponentsialnosti, svobodnykh ot parametra masshtaba, Kandidatskaya dissertatsiya, SPbGU, 2005, 82 pp.

[6] R. R. Bahadur, “Rates of convergence of estimates and test statistics”, Ann. Math. Stat., 38 (1967), 303–324 | DOI | MR | Zbl

[7] P. L. Janssen, Generalized empirical distribution functions with statistical applications, Limburgs Universitair Centrum, Diepenbeek, 1988

[8] Ya. Yu. Nikitin, “Large deviations of $U$-empirical Kolmogorov–Smirnov tests, and their efficiency”, J. Nonparam. Statistics, 2010 (to appear) ; Доступно в arxiv: 0906.0428[math.PR] | MR

[9] Ya. Yu. Nikitin, “$U$-statistical Kolmogorov–Smirnov tests: large deviations and asymptotic efficiency”, Proceedings of ISNI2008, eds. J. C. Fernandez-Pardo, J. de Una-Alvarez, Vigo, 2008, 138–142

[10] Ya. Yu. Nikitin, A. V. Tchirina, “Bahadur efficiency and local optimality of a test for the exponential distribution based on the Gini statistic”, J. Ital. Statist. Soc., 5:1 (1996), 163–175 | DOI | Zbl

[11] H.-J. Rossberg, “Characterization of the exponential and the Pareto distributions by means of some properties of the distributions which differences and quotients of order statistics are subjected to”, Math. Operat. Statist., 3 (1972), 207–216 | DOI | MR | Zbl

[12] M. Riedel, H.-J. Rossberg, “Characterization of the exponential distribution function by properties of the difference $X_{k+s:n}-X_{k:n}$ of order statistics”, Metrika, 41 (1994), 1–19 | DOI | MR | Zbl

[13] B. W. Silverman, “Convergence of a class of empirical distribution functions of dependent random variables”, Ann. Probab., 11 (1983), 745–751 | DOI | MR | Zbl