A note on optimal estimation in the presence of outliers

الملخص EN

The basic estimation problem of the mean and standard deviation of a random normal process in the presence of an outlying observation is considered.

The value of the outlier is taken as a constraint imposed on the maximization problem of the log likelihood.

It is shown that the optimal solution of the maximization problem exists and expressions for the estimates are given.

Applications to estimation in the presence of outliers and outlier detection are discussed and illustrated through a simulation study and analysis of trade data.