Information in Quantal Response Data and Random Censoring

In this paper we study interesting properties of Fisher and divergence type measures of information for quantal, complete and incomplete random censoring, and not censoring at all. It is shown that, while quantal random censoring is less expensive, it is less informative than complete random censoring. It is also shown that in experiments which are mixtures of quantal and complete random censoring, the information received from these experiments is a convex combination of quantal information and the information in complete random censoring. Finally, the "total information" property is studied, in which the information received by the uncensored experiment can be expressed as the sum of the information provided by random censoring and the loss of information due to censoring. The results for Fisher's measure of information are an extension of already known results to the multiparameter case. The investigation of the previous information properties for divergence type measures is a new element, as well as the comparison of byproducts of Fisher information matrices.