Geodesic
On entropy estimation by $m$-spacing method
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 151-181 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The $m$-spacing method is a very popular statistical tool in entropy estimation and in goodness of fit testing. In this text, we focus on the case, where the underlying probability density may have an unbounded support or may vanish and show that under mild conditions the $m$-spacing entropy estimators have standard Gaussian limits. Bibl. – 15 titles. 
@article{ZNSL_2009_363_a8,
     author = {F. El Haje Hussein and Yu. Golubev},
     title = {On entropy estimation by $m$-spacing method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--181},
     year = {2009},
     volume = {363},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a8/}
}
TY  - JOUR
AU  - F. El Haje Hussein
AU  - Yu. Golubev
TI  - On entropy estimation by $m$-spacing method
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 151
EP  - 181
VL  - 363
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a8/
LA  - en
ID  - ZNSL_2009_363_a8
ER  - 
%0 Journal Article
%A F. El Haje Hussein
%A Yu. Golubev
%T On entropy estimation by $m$-spacing method
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 151-181
%V 363
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a8/
%G en
%F ZNSL_2009_363_a8
F. El Haje Hussein; Yu. Golubev. On entropy estimation by $m$-spacing method. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 151-181. http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a8/

[1] J. Beirlant, “Limit theory for spacings og order statistics from general univariate distribution”, Publ. Inst. Stat. Univ. Paris, 31:1 (1986), 27–57 | MR | Zbl

[2] J. Beirlant, M. C. A. van Zuijlen, “The impirical distribution function and strong laws for functions of order statistics of uniform spacings”, J. Multivar. Anal., 16 (1985), 300–317 | DOI | MR | Zbl

[3] N. Cressie, “On the logarithm of high-order spasings”, Biometrica, 63:2 (1976), 343–355 | DOI | MR | Zbl

[4] D. A. Darling, “On a class of problems related to the random division of an interval”, Ann. Math. Statist., 24 (1953), 239–253 | DOI | MR | Zbl

[5] P. Deheuvels, G. Derzko, “Exact laws for sums of logarithms of uniform spacings”, Austr. J. Statist., 32:1–2 (2003), 29–47

[6] F. El Haje, Yu. Golubev, P.-Y. Liardet, Ya. Teglia, “On statistical testing of random numbers generators”, Security and Criptography for Networks, eds. De Prisco R., Yung M., Springer-Verlag, Berlin–Heidelberg, 2006, 271–287 | DOI | Zbl

[7] R. Hasminskii, I. Ibragimov, “On the nonparametric estimation of functionals”, Proc. II Prague Symp. Asymptotic Statistics, 1978, 41–51 | MR

[8] I. Ibragimov, R. Khasminskii, Statistical Estimation: Asymptotic Theory, Springer-Verlag, 1981 | MR | Zbl

[9] I. Ibragimov, A. Nemirovski, R. Khasminskii, “Some problems of nonparametric estimation in Gaussian white noise”, Theory Probab. Appl., 31:3 (1986), 391–406 | DOI | MR

[10] L. F. Kozachenko, N. N. Leonenko, “On statistical estimation of entropy of a random vector”, Probl. Inform. Transmission, 23 (1987), 95–101 | MR | Zbl

[11] B. Levit, “On the efficiency of a class of nonparametric estimates”, Theor. Probab. and Applic., 20 (1975), 723–740 | DOI | MR | Zbl

[12] A. Nemirovski, “Topics in Nonparametric Statistics”, M. Emery, A. Nemirovski, D. Voiculescu, Lectures on Probability Theory and Statistics, Ecole d'ete de Probabilities (Saint-Flour XXVIII, 1998), Lect. Notes in Math., 1738, ed. P. Bernard, Springer-Verlag, 2000, 85–277 | MR | Zbl

[13] R. Pyke, “Spacings (with discussion)”, J. R. Statist. Soc., 7 (1965), 395–449 | MR

[14] A. B. Tsybakov, E. C. Van der Meulen, Root-$n$ consistent estimators of entropy for densities with unbounded supprot, Discussion paper 9206, Universié Catholique de Louvain, 1992

[15] A. W. Van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998 | MR