An adaptive smoothing estimator lor probabilities in contingency tables

Abstract

We present an estimator for the vector p of cell probabilities in a k-dimensional contingency table, which is based on smoothing an estimate of the vector q describing the interpendences, while estimating the one-dimensional marginal distributions by the observed frequencies. The background for this estimator is the realistic situation, in which no reliable prior information is available on the structure of the contingency table or the corresponding probabilities and there is at most the hope, that the q values at neighbouring.

Keywords:

• Multinomial distribution
• multinomial parameter estimation
• kernel estima¬tors
• iterative proportional scaling