The method of variants deals with populations whose members are represented by more than one feature set, each, only one of which is a valid representation. We call these feature sets variants of the object. In this communication, we are concerned with point estimation in the presence of variants. Besides parameter estimation, this involves also selecting the valid feature set (regular variant). We determine mixed MAP--ML estimators for three different statistical models with normal regular variants. Our methods consist of maximum likelihood estimation for incomplete data, linear regression for monotone data patterns, and the EM--algorithm. The estimators turn out to be computationally hard; therefore, we design algorithms for their efficient approximation. These are based on the arithmetic--geometric inequality for positive semi--definite matrices.
Nathalie Vollstaedt