Profile Statistics for Sparse Contingency Tables under Poisson Sampling
DOI:
https://doi.org/10.17713/ajs.v40i1&2.203Abstract
Simple conditions for the inconsistency of classical likelihood ratio (LR) test in case of very sparse categorical data are given. The LR type test based on profile statistics is proposed as an alternative. The performance of both tests for a sparse contingency table is compared by simulations.References
Agresti, A. (1990). Categorical Data Analysis. New York: Wiley & Sons.
Agresti, A. (1999). Exact inference for categorical data: recent advances and continuing controversies. Statistical Methods and Applications, 20, 2709-2722.
Agresti, A., and Hitchcock, B. D. (2005). Bayes inference for categorical data analysis. Statistical Methods and Applications, 14, 297-330.
Congdon, P. (2005). Bayesian Models for Categorical Data. New York: Wiley & Sons.
Coull, B. A., and Agresti, A. (2003). Generalized log-linear models with random effects, with application to smoothing contingency tables. Statistical Modelling, 3, 251-271.
Cressie, N., and Read, T. (1984). Multinomial goodness of fit tests. Journal of the Royal Statistical Society, 46, 440-464.
Hu, M. Y. (1999). Model Checking for Incomplete High Dimensional Categorical Data. Unpublished doctoral dissertation, University of California, Los Angeles.
Khmaladze, E. (1988). The statistical analysis of a large number of rare events (Report No. MS-R8804). Amsterdam.
Kolchin, V. F., Sevastyanov, B., and Chistyakov, V. (1978). Random Allocations. New York: Wiley.
Kuss, O. (2002). Global goodness-of-fit tests in logistic regression with sparse data. Statistics in Medicine, 21, 3789-3801.
Müller, U. U., and Osius, G. (2003). Asymptotic normality of goodness-of-fit statistics for sparse Poisson data. Statistics, 37, 119-143.
Sanov, I. (1957). On the probability of large deviations of random magnitudes. Mat. Sb. N. S., 42, 11-44.
Smirnoff, J. S. (1995). Smoothing categorical data. Journal of Statistical Planning and Inference, 47, 41-69.
van de Geer, S. (2003). Asymptotic theory for maximum likelihood in nonparametric mixture models. Computational Statistics and Data Analysis, 41, 453-464.
van Es, B., Klaassen, C. A. J., and Mnatsakanov, R. M. (2003). Estimating the structural distribution function of cell probabilities. Austrian Journal of Statistics, 32, 85-98.
von Davier, M. (1997). Bootstraping goodness-of-fit statistics for sparse categorical data. Results of a Monte Carlo study (Vol. 2). Available from http//www.pabst-publishers.de/mpr/
Downloads
Published
How to Cite
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.