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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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  and Kapur . 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
|Subjects:||Sciences > Mathematics > Mathematical statistics|
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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