New family of estimators for the loglinear model of quasi-independence based on power-divergence measures

Abstract

In this paper, we study the minimum power-divergence estimator, introduced and studied by Cressie and Read [Cressie, N. and Read, T.R.C., 1984, Multinomial goodness-of-fit tests. Journal of the Royal Statistic Society, Series B, 46, 440–464.], in the loglinear model of quasi-independence. A simulation study illustrates that minimum chi-squared estimator and Cressie–Read estimator are good alternatives to the classical maximum-likelihood estimator for this problem. The estimator obtained for λ=2 is the most robust and efficient estimator among the family of the minimum power estimators.

Keywords:

• Loglinear model
• Quasi-independence
• Maximum likelihood
• Minimum power-divergence estimator

Acknowledgements

We would like to thank the referee and editor for their helpful comments. This work was supported by grant DGES PB2003-892 and UCM 2005-910707.