MAXIMUM-LIKELIHOOD REGRESSION ON RELEVANT COMPONENTS

Most regression methods for multicollinear data are only based on assu mptions about the conditional distribution of the dependent variable, given the explanatory variables. Here we propose a new prediction meth od taking a joint multinormal distribution for all the variables as th e starting point. A hypothesis is formulated stating that only a fixed small number of components constructed from the explanatory variables is relevant for prediction, and maximum-likelihood-type estimates of the parameters in the model are developed under this hypothesis.