INFERENCE PROCEDURES FOR THE SYMMETRY IN A CONTINGENCY TABLE

Several inference procedures are discussed for the partial sym metry and the complete symmetry in a twodimensional contingency table. The inference procedures proposed in the present paper is firstly to select a model fitted to observed frequencies, and secondly to estimate the parameters of the selected model. Such procedures are also called those of the preliminary test estimation in the situa tion that an estimation follows a testing. We consider here the op timality of significance levels for the inference procedures based on the theory of minimax regret, and compare the optimal significance level with that based on AIC. Finally we propose a weighted estimate method for a contingency table, as a modification of the preliminary test estimation.