On the construction of a parameter orthogonal to the mean

Abstract

It is shown that for many parametric families the condition for a parameter to be orthogonal to the mean takes on a particularly simple form. As a result, it is often possible to obtain analytically an explicit orthogonal parameter, thus providing insight into the many situations involving parametric families in which such a parameter is known to exist. Orthogonal parameterizations are then given for some other models.