A Note on Penalized Power-Divergence Test Statistics

Authors: Aylin Alin

Abstract:

In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized power-divergence test statistics have the same asymptotic distribution, comparisons have been only made for small and moderate samples. Three-way contingency tables distributed according to a multinomial distribution have been considered. Simulation results reveal that penalized power-divergence test statistics perform much better than their ordinary counterparts.

Keywords: Contingency table, Log-linear models, Penalization, Power-divergence measure, Penalized power-divergence measure.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071418

References:

[1] Cressie, N., and Read, T. R. C., ''Multinomial Goodness-of-Fit Tests,'' Journal of Royal Statistical Society B, vol. 46, pp. 440-464, 1984.
[2] Basu, A., and Basu, S., ''Penalized Minimum Disparity Methods for Multinomial Models,'' Statistica Sinica, vol. 8, pp. 841-860, 1998.
[3] Pardo, L., and Pardo, M. D. C., ''Minimum Power-Divergence Estimator in Three-Way Contingency Tables,'' Journal of Statistical Computation Simulation, vol. 73, pp. 819-831, 2003.
[4] Cressie, N., and Pardo, L.,''Minimum ¤å-divergence Estimator and Hierarchical Testing in Loglinear models,'' Statistica Sinica, vol.10, pp. 867-884, 2000.