Outlier detection through mixtures with an improper component

The paper investigates the use of a finite mixture model with an addi- tional uniform density for outlier detection and robust estimation. The main contribution of this paper lies in the analysis of the properties of the im- proper component and the introduction of a modified EM algorithm which, beyond providing the maximum likelihood estimates of the mixture parame- ters, endogenously provides a numerical value for the density of the uniform distribution used for the improper component. The mixing proportion of outliers may be known or unknown. Applications to robust estimation and outlier detection will be discussed with particular attention to the normal mixture case.