Pardo Llorente, Julio Ángel and Pardo Llorente, María del Carmen (2008) Minimum phi-divergence estimator and phi-divergence statistics in generalized linear models with binary data. Methodology and computing in applied probability, 10 (3). pp. 357-379. ISSN 1387-5841
Restricted to Repository staff only until 2020.
In this paper, we assume that the data are distributed according to a binomial distribution whose probabilities follow a generalized linear model. To fit the data the minimum phi-divergence estimator is studied as a generalization of the maximum likelihood estimator. We use the minimum phi-divergence estimator, which is the basis of some new statistics, for solving the problems of testing in a generalized linear model with binary data. A wide simulation study is carried out for studying the behavior of the new family of estimators as well as of the new family of test statistics.
|Uncontrolled Keywords:||generalized linear model; chi-squared distribution; binomial distribution; phi-divergence measure; nested sequence|
|Subjects:||Sciences > Mathematics > Mathematical statistics|
S. M. Ali, and S. D. Silvey, “A general class of coefficients of divergence of one distribution from another,” Journal of the Royal Statistical Society, Series B vol. 26 pp. 131–142, 1966.
E. B. Andersen, Introduction to the Statistical Analysis of Categorical Data I, Springer 1997.
A. Basu, and S. Basu, “Penalized minimum disparity methods for multinomial models,” Statistica Sinica vol. 8 pp. 841–860, 1998.
S. K. Bhandari, A. Basu, and S. Sarkar, “Robust inference in parametric model using the family of generalized negative exponential disparities,” Australian and New Zealand Journal of Statistics vol. 48 pp. 95–114, 2006.
B. Bhattacharya, “Csiszár divergence from constant failure rate model for grouped data,” Communications Statistics Theory and Methods vol. 30(6) pp. 1131–1141, 2001.
B. Bhattacharya, and A. Basu, “Disparity based goodness-of-fit tests for and against restrictions for multinomial models,” Journal Nonparametric Statistic vol. 15(1) pp. 1–10, 2003.
H. S. Chen, K. Lai, and A. Ying, “Goodness-of-fit and minimum power divergence estimation for survival data,” Statistica Sinica vol. 14 pp. 231–248, 2004.
N. A. C. Cressie, and L. Pardo, “Minimum φ-divergence estimator and hierarchical testing in loglinear models,” Statistica Sinica vol. 10 pp. 867–884, 2000.
N. A. C. Cressie, and L. Pardo, “Phi-divergence statistics,” In A. H. ElShaarawi and W. W. Piegorich (eds.), Encyclopedia of Environmetrics, vol. 3 pp. 1551–555, Wiley: New York, 2002.
N. A. C. Cressie, L. Pardo, and M. C. Pardo, “Size and power considerations for testing loglinear models using φ-divergence test statistics,” Statistica Sinica vol. 17(5) pp. 555–570, 2003.
I. Csiszár, “Eine Informationtheorestiche Ungleichung und ihre Anwendung anf den Beweis der Ergodizität Markoffshen Ketten,” Publications of the mathematical Institute of Hungarian Academy of Sciences, Series A vol. 8 pp. 84–108,1963.
J. R. Dale, “Asymptotic normality of goodness-of-fit statistics for sparse product multinomials,”Journal of the Royal Statistical Society, Series B vol. 41 pp. 48–59, 1986.
T. S. Ferguson, A Course in Large Sample Theory, Wiley: New York, 1996.
K. Fokianos, “Power divergence family of tests for categorical time series models,” Annals of the Institute of Statistical Mathematics vol. 54 pp. 543–564, 2002.
S. Kullback, “Kullback information,” In S. Kotz and N. L. Johnson (eds.), Encyclopedia of Statistical Sciences, vol. 4 pp. 421–425, Wiley: New York, 1985.
M. L. Menéndez, J. A. Pardo, and L. Pardo, “Tests for bivariate symmetry against ordered alternatives in square contingency tables,” Australian and New Zealand Journal of Statistics vol. 45(1)pp. 115–124, 2003.
M. L. Menéndez, J. A. Pardo, L. Pardo, andK. Zografos, “On tests of symmetry, marginal homogeneity and quasi-symmetry in two-way contingency tables based onminimum −divergence estimator with constraints,” Journal of Statistical Computation and Simulation vol. 75(7) pp. 555–580, 2005.
I. Molina, and D. Morales, “Rényi statistics for testing hypotheses in mixed linear regression models,”Journal of Statistical Planning and Inference vol. 137 pp. 87–102, 2006.
D. Morales, L. Pardo, and I. Vajda, “Asymptotic divergence of estimates of discrete distributions,”Journal Statistical Planning and Inference vol. 48 pp. 347–369, 1995.
D. Morales, L. Pardo, and I. Vajda, “Some new statistics for testing hypotheses in parametric models,” Journal of Multivariate Analysis vol. 62(1) pp. 137–168, 1997.
J. Muñoz-Garcia, J. M. Muñoz-Pichardo, and L. Pardo “Cressie and read power-divergences as influence measures for logistic regression model,” Computational Statistics and Data Analysis vol. 50, pp. 3199–3221, 2006.
J. A. Pardo, L. Pardo, and M. C. Pardo, “Minimum φ-divergence estimator in logistic regression models,” Statistical Papers vol. 47 pp. 91–108, 2005.
J. A. Pardo, L. Pardo, andM. C. Pardo, “Testing in logistic regression models based on φ-divergences measures,” Journal of Statistical Planning and Inference vol. 136 pp. 982–1006, 2006.
L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall, 2006.
L. Pardo, and M. C. Pardo, “Nonadditivity in loglinear models using φ-divergences and MLEs,”Journal of Statistical Planning and Inference vol. 127(1–2) pp. 237–252, 2005.
M. C. Pardo, “On Burbea-Rao divergence based goodness-of-fit tests for multinomial models,”Journal of Multivariate Analysis vol. 69(1) pp. 65–87, 1999.
W. C. Parr, “Minimum distance estimation: a bibliography,” Communications in Statistics (Theory and Methods) vol. 10 pp. 1205–1224, 1981.
T. R. C. Read, and N. A. C. Cressie, Goodness-of-fit Statistics for Discrete Multivariate Data, Springer: New York, 1988.
M. J. Rivas, M. T. Santos, and D. Morales, “Rényi test statistics for partially observed diffusion processes,” Journal of Statistical Planning and Inference vol. 127 pp. 91–102, 2005.
I. Vajda, Theory of Statistical Inference and Information, Kluwer: Boston, 1989.
|Deposited On:||05 Dec 2012 09:35|
|Last Modified:||07 Feb 2014 09:45|
Repository Staff Only: item control page