On estimating the center of the Student distribution with a small number degrees of freedom (Q1878778)

The paper considers a symmetric family of distributions with ``heavy tails,'' which, for example, contains the Cauchy distribution, or, more precisely, the Student distribution with small degrees of freedom. It is assumed that the shape parameter (the number of degrees of freedom) is known, while the center of the distribution is unknown and must be determined. The authors obtain equivariant estimators for the center (\(M\) estimators) and maximum likelihood estimators. Their asymptotic relative effectivity is found, and their behavior is studied for a small number of the degrees of freedom.