Parameter estimation under ambiguity and contamination with the spurious model

Recently, we proposed variants as a statistical model for treating ambiguity. If data are extracted from an object with a machine then it might not be able to give a unique safe answer due to ambiguity about the correct interpretation of the object. On the other hand, the machine is often able to produce a finite number of alternative feature sets (of the same object) that contain the desired one. We call these feature sets variants of the object. Data sets that contain variants may be analyzed by means of statistical methods and all chapters of multivariate analysis can be seen in the light of variants. In this communication, we focus on point estimation in the presence of variants and outliers. Besides robust parameter estimation, this task requires also selecting the regular objects and their valid feature sets (regular variants). We determine the mixed MAP–ML estimator for a model with spurious variants and outliers as well as estimators based on the integrated likelihood. We also prove asymptotic results which show that the estimators are nearly consistent. oblem of variant selection turns out to be computationally hard; therefore, we also design algorithms for efficient approximation. We finally demonstrate their efficacy with a simulated data set and a real data set from genetics.