Estimation of the Mean of a Univariate Normal Distribution When the Variance is not Known

We consider the problem of estimating the first k coeffcients in a regression equation with k + 1 variables.For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002).We investigate properties of this estimator in the case where the unknown variance is estimated by least squares.We find that the optimality properties of the Laplace estimator only change marginally.Therefore we recommend the neutral Laplace estimator to be used in practice.