Distributional least squares based on the generalized lambda distribution

Ordinary least squares is an optimal procedure in many senses when the stochastic component has a Gaussian distribution or when linear estimates are required (Gauss-Markov Theorem). Nevertheless, departures from normality are quite plausible in many situations. In this paper, we propose an iterative proce- dure for estimating the regression coefficients modelling the residual term by a five-parameter version of the generalized lambda distribution. Distributional and regression parameters are estimated in a unique procedure and the effectiveness of the technique is analyzed on real and simulated data.