Geodesic
Goodness-of-fit tests based on $K_\phi$-divergence
Kybernetika, Tome 39 (2003) no. 6, pp. 739-752 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper a new family of statistics based on $K_{\phi }$-divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum $K_{\phi }$-divergence.
In this paper a new family of statistics based on $K_{\phi }$-divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum $K_{\phi }$-divergence.
Classification : 62B10, 62E20, 62F03, 62G10
Keywords: $K_{\phi }$-divergence; goodness-of-fit; minimum $K_{\phi }$-divergence estimate 
@article{KYB_2003_39_6_a5,
     author = {P\'erez, Teresa and Pardo, Julio A.},
     title = {Goodness-of-fit tests based on $K_\phi$-divergence},
     journal = {Kybernetika},
     pages = {739--752},
     year = {2003},
     volume = {39},
     number = {6},
     mrnumber = {2035648},
     zbl = {1243.62062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_6_a5/}
}
TY  - JOUR
AU  - Pérez, Teresa
AU  - Pardo, Julio A.
TI  - Goodness-of-fit tests based on $K_\phi$-divergence
JO  - Kybernetika
PY  - 2003
SP  - 739
EP  - 752
VL  - 39
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_6_a5/
LA  - en
ID  - KYB_2003_39_6_a5
ER  - 
%0 Journal Article
%A Pérez, Teresa
%A Pardo, Julio A.
%T Goodness-of-fit tests based on $K_\phi$-divergence
%J Kybernetika
%D 2003
%P 739-752
%V 39
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_6_a5/
%G en
%F KYB_2003_39_6_a5
Pérez, Teresa; Pardo, Julio A. Goodness-of-fit tests based on $K_\phi$-divergence. Kybernetika, Tome 39 (2003) no. 6, pp. 739-752. http://geodesic.mathdoc.fr/item/KYB_2003_39_6_a5/

[1] Birch N. W.: A new proof of the Pearson-Fisher theorem. Ann. Math. Statist. 35(1964), 817–824 | DOI | MR | Zbl

[2] Bishop Y. M. M., Fienberg S. E., Holland P. W.: Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge, MA 1975 | MR | Zbl

[3] Burbea J.: J-divergences and related topics. Encyclopedia Statist. Sci. 44 (1983), 290–296

[4] Burbea J., Rao C. R.: On the convexity of some divergence measures based on entropy functions. IEEE Trans. Inform. Theory 28 (1982), 489–495 | DOI | MR | Zbl

[5] Cressie N. C. T. R.: Multinomial Goodness-of-fit Tests. J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464 | MR | Zbl

[6] Csiszár I.: Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar. 2 (1967), 299–318 | MR

[7] Fraser D. A. S.: Nonparametric methods in Statistics. Wiley, New York 1957 | MR | Zbl

[8] Fryer J. C., Robertson C. A.: A comparison of some methods for estimating mixed normal distributions. Biometrika 59 (1972), 639–648 | DOI | MR | Zbl

[9] Morales D., Pardo, L., Vajda I.: Asymptotic divergence of estimates of discrete distributions. J. Statist. Plann. Inference 48 (1995), 347–369 | DOI | MR | Zbl

[10] Pardo M. C.: On Burbea-Rao divergence based goodness-of-fit tests for multinomial models. J. Multivariate Anal. 69 (1999), 65–87 | DOI | MR | Zbl

[11] Pérez T., Pardo J. A.: The $K_{\phi }$ -divergence statistics for categorical data problem. Submitted

[12] Pérez T., Pardo J. A.: Minimum $K_{\phi }$ -divergence estimator. Appl. Math. Lett. (to appear) | MR | Zbl

[13] Rao C. R.: Diversity and dissimilarity coefficients: a unified approach. J. Theoret. Population Biology 21 (1982), 24–43 | DOI | MR | Zbl

[14] Rao J. N. K., Scott A. J.: The analysis of categorical data from complex sample surveys: chi-squared tests for goodness of fit and independence in two-way tables. J. Amer. Statist. Assoc. 76 (1981), 221–230 | DOI | MR | Zbl

[15] Read T. R. C., Cressie N. A. C.: Goodness of fit Statistics for discrete multivariate data. Springer–Verlag, Berlin 1988 | MR | Zbl

[16] Vajda T., Vašek K.: Majorization, concave entropies, and comparison of experiments. Prob. Control Inform. Theory 14 (1985), 105–115 | MR

[17] Zografos K., Ferentinos, K., Papaioannou T.: $\varphi $ -divergence statistics: sampling properties and multinomial goodness of fit divergence tests. Comm. Statist. Theory Methods 19 (1990), 5, 1785–1802 | DOI | MR