An algorithm for robust linear estimation with grouped data

Abstract

An algorithm which is valid to estimate the parameters of linear models under several robust conditions is presented. With respect to the robust conditions, firstly, the dependent variables may be either non-grouped or grouped. Secondly, the distribution of the errors may vary within the wide class of the strongly unimodal distributions, either symmetrical or non-symmetrical. Finally, the variance of the errors is unknown. Under these circumstances the algorithm is not only capable of estimating the parameters (slopes and error variance) of the linear model, but also the asymptotic covariance matrix of the linear parameters. This opens the possibility of making inferences in terms of either multiple confidence regions or hypothesis testing