Landaburu Jiménez, María Elena and Pardo Llorente, Leandro
(2000)
*Goodness of fit tests with weights in the classes based on (h,phi)-divergences.*
Kybernetika , 36
(5).
pp. 589-602.
ISSN 0023-5954

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## Abstract

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted (h, phi)-divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [5] and Kapur [11]. The weighted (h, phi)-divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear combination of independent chi-square variables. Some approximations to the linear combination of independent chi-square variables are presented

Item Type: | Article |
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Uncontrolled Keywords: | Divergence |

Subjects: | Sciences > Mathematics > Mathematical statistics |

ID Code: | 16512 |

References: | I. Csiszar: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten. Publications of the Mathematical Institute of Hungarian Academy of Sciences Ser A. 8 (1963), 85-108. J. J. Dik and M. C. M. de Gunst: The distribution of general quadratic forms in normal variables. Statistica Neerlandica 39 (1985), 14-26. A. R. Eckler: A survey of coverage problems associated with point and area targets. Technometrics 11 (1969), 561-589. T. S. Ferguson: A Course in Large Sample Theory. Chapman & Hall, London 1996. O. Frank, M. L. Menendez and L. Pardo: Asymptotic distributions of weighted divergence between discrete distributions. Comm. Statist. - Theory Methods 21 (1998), 4, 867-885. D. A.S. Fraser: Non-parametrics Methods in Statistics. Wiley, New York 1957. S. Guia§u: Grouping data by using the weighted entropy. J. Statist. Plann. Inference I5(1986), 63-69. S.S. Gupta: Bibliography on the multivariate normal integrals and related topics. Ann. Math. Statist. 34 (1963), 829-838. D.R. Jensen and H. Solomon: A Gaussian approximation to the distribution of a definite quadratic form. J. Amer. Statist. Assoc. 57(1972), 340, 898-902. N.L. Johnson and S. Kotz: Tables of distributions of positive definite quadratic forms in central normal variables. Sankhya, Ser. B SO (1968), 303-314. J.N. Kapur: Measures of Information and their Applications. Wiley, New York 1994. S. Kotz, N.M. Johnson and D.W. Boid: Series representation of quadratic forms in normal variables I. Central case. Annals Math. Statist. 38 (1967), 823-837. F. Liese and I. Vajda: Convex Statistical Distances. Teubner, Leipzig 1987. G. Longo: Quantitative and Qualitative Measure of Information. Springer, New York 1970. M. L. Menendez, D. Morales, L. Pardo and M. Salicrii: Asymptotic behaviour and statistical applications of divergence measures in multinomial populations: A unified stydy. Statistical Papers 55 (1995). 1-29. M. L. Menendez, D. Morales, L. Pardo and I. Vajda: Approximations to powers of (^-disparity goodness of fit tests. Submitted. R. Modarres and R. W. Jernigan: Testing the equality of correlation matrices. Comm. Statist. - Theory Methods 21 (1992), 2107-2125. J.N.K. Rao and A.J. Scott: 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 75(1981), 221-230. H. Solomon: Distribution of Quadratic Forms - Tables and Applications. Applied Mathematics and Statistics Laboratories, Technical Report 45, Stanford University,Stanford, Calif.1960. C T . Taneja: On the mean and the variance of estimates of Kullback information and relative useful information measures. Apl. Mat. SO (1985), 166-175. I. Vajda: Theory of Statistical Inference and Information. Kluwer Academic Publishers, Dordrecht 1989. K. Zografos, K. Ferentinos and Papaioannou: (^-divergence statistics: sampling properties and multinomial goodness of fit and divergence tests. Comm. Statist. - Theory Methods 19 (1990), 5, 1785-1802. |

Deposited On: | 25 Sep 2012 08:46 |

Last Modified: | 07 Feb 2014 09:30 |

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