On the asymptotic properties of a nonparametric L1-test statistic of homogeneity

IEEE Transactions on Information Theory

Volumn 51, Issue 11, 2005, Pages 3965-3973

  Biau, Gérard ^a   Györfi, László ^b  

^a UNIVERSITÉ DE MONTPELLIER   (France)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Central limit theorem; Consistent testing; Homogeneity testing; Large deviations; Partitions; Poissonization

Indexed keywords

ASYMPTOTIC STABILITY; PROBABILITY; RANDOM PROCESSES; SET THEORY; STATISTICAL METHODS;

CENTRAL LIMIT THEOREM; CONSISTENT TESTING; HOMOGENEITY TESTING; LARGE DEVIATIONS; POISSONIZATION;

INFORMATION THEORY;

EID: 27744479466     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.856979     Document Type: Article

References (20)

1. P. E. Greenwood and M. S. Nikulin, A Guide to Chi-Squared Testing. New York: Wiley, 1996.
2. M. C. Pardo, L. Pardo, and I. Vajda, "Testing Homogeneity of Independent Samples From Arbitrary Models," Institute of Automation and Information Theory of the Czech Academy of Sciences, Prague, Czech Republic, Res. Rep. 2104, 2004.
3. T.R.C.ReadandN.A.C.Cressie,Goodness-of-fitStatisticsforDiscrete Multivariate Data. Berlin, Germany: Springer-Verlag, 1988.
4. L. Pardo, M. C. Pardo, and K. Zografos, "Homogeneity for multinomial populations based on ó-divergences," J. Japan Statist. Soc., vol. 29, pp. 213-228, 1999.
5. L. Györfi and E. C. van der Meulen, "A consistent goodness of fit test based on the total variation distance," in Nonparametric Functional Estimation and Related Topics, G. Roussas, Ed. Dordrecht, The Netherlands: Kluwer, 1990, pp. 631-645.
6. 2-errors in histogram density estimation," Canad. J. Statist., vol. 22, pp. 309-318, 1994.
7. J. Beirlant, L. Devroye, L. Györfi, and I. Vajda, "Large deviations of divergence measures on partitions," J. Statist. Plann. Inference, vol. 93, pp. 1-16, 2001.
8. L. Devroye and L. Györfi, "Distribution and density estimation," in Principles of Nonparametric Learning, L. Györfi, Ed. Wien, Austria: Springer-Verlag, 2002, pp. 223-286.
9. H. Scheffé, "A useful convergence theorem for probability distributions," Ann. Math. Statist., vol. 18, pp. 434-438, 1947.
10. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed. New York: Springer-Verlag, 1998.
11. A. Dembo and Y. Peres, "A topological criterion for hypothesis testing," Ann. Statist., vol. 22, pp. 106-117, 1994.
12. L. Devroye and G. Lugosi, "Almost sure classification of densities," J. Nonparametr. Statist., vol. 14, pp. 675-698, 2002.
13. A. R. Barron, L. Györfi, and E. C. van der Meulen, "Distribution estimation consistent in total variation and in two types of information divergence," IEEE Trans. Inf. Theory, vol. 38, no. 5, pp. 1437-1454, Sep. 1992.
14. L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition. New York: Springer-Verlag, 1996.
15. M. S. Bartlett, "The characteristic function of a conditional statistic," J. London Math. Soc., vol. 13, pp. 62-67, 1938.
16. p-norms of empirical functionals," Math. Methods Statist., vol. 4, pp. 1-19, 1995.
17. 1-norm density estimator process," Ann. Probab., vol. 31, pp. 719-768, 2003.
18. C. R. Rao, Statistical Inference and its Applications, 2nd ed. New York: Wiley, 1973.
19. T. J. Sweeting, "Speeds of convergence for the multidimensional central limit theorem," Ann. Probab., vol. 5, pp. 28-41, 1977.
20. I. S. Shiganov, "Refinement of the upper bound of the constant in the central limit theorem (English)," J. Sov. Math., vol. 35, pp. 2545-2550, 1986.