Publication: New families of estimators and test statistics in log-linear models
Loading...
Full text at PDC
Publication Date
2008-09
Authors
Martín Apaolaza, Níriam
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Academic Press
Citations
Exportar
Abstract
In this paper we consider categorical data that are distributed according to a multinomial, product-multinomial or Poisson distribution whose expected values follow a log-linear model and we study the inference problem of hypothesis testing in a log-linear model setting. The family of test statistics considered is based on the family of phi-divergence measures. The unknown parameters in the log-linear model under consideration are also estimated using phi-divergence measures: Minimum phi-divergence estimators. A simulation study is included to find test statistics that offer an attractive alternative to the Pearson chi-square and likelihood-ratio test statistics.
Description
UCM subjects
Unesco subjects
Keywords
Citation
A. Agresti, An Introduction to Categorical Data Analysis, John Wiley & Sons, New York, 1996. MR1394195 (97c:62133)
A. Agresti, Categorical Data Analysis, John Wiley & Sons, New York, 2002.
R. Christensen, Log-Linear Model and Logistic Regression, Springer-Verlag, New York, 1997.
N. Cressie, L. Pardo, Minimum φ-divergence estimator and hierarchical testing in loglinear models, Statistica Sinica 10 (2000) 867–884.
N. Cressie, L. Pardo, Model checking in loglinear models using φ-divergences and MLEs, Journal of Statistical Planning and Inference 103 (2002) 437–453.
N. Cressie, L. Pardo, M.C. Pardo, Size and power considerations for testing loglinear models using φ-divergence test statistics, Statistica Sinica 13 (2003) 555–570.
N. Cressie, T.R.C. Read, Multinomial goodness-of-fit tests, Journal of the Royal Statistical Society Series B 46 (1984) 440–464.
J.R. Dale, Asymptotic normality of goodness-of-fit statistics for sparse product multinomials, Journal of the Royal Statistical Society Series B 41 (1986) 48–59. MR0848050 (88f:62058)
T.S. Ferguson, A Course in Large Sample Theory, Texts in Statistical Science, Chapman & Hall, London, 1996.
A.K. Gupta, T. Nguyen, L. Pardo, Residual analysis and outliers in loglinear models based on phi-divergence statistics, Journal of Statistical Planning and Inference 137 (2007) 1407–1423.
S.J. Haberman, The Analysis of Frequency Data, University of Chicago Press, Chicago, 1974.
J.B. Lang, On the comparison of multinomial and Poisson log-linear models, Journal of the Royal Statistical Society Series B 58 (1996) 253–266.
N. Martín, L. Pardo, Minimum Phi-divergence estimators for loglinear models with linear constraints and multinomial sampling, Statistical Papers 49 (2008) 15–36.
I. Molina, D. Morales, Rényi statistics for testing hypotheses in mixed linear regression models, Journal of Statistical Planning and Inference 137 (2007) 87–102.
L. Pardo, Statistical Inference based on Divergence Measures, in: Textbooks and Monographs, Chapman & Hall/CRC, New York, 2006.
S.R. Searle, Linear Models, John Wiley & Sons, New York, 1971.