A two step model for linear prediction, with connections to PLS

Sammanfattning: In the thesis, we consider prediction of a univariate response variable, especially when the explanatory variables are almost collinear. A two step approach has been proposed. The first step is to summarize the information in the explanatory variables via a bilinear model with a Krylov structured design matrix. The second step is the prediction step where a conditional predictor is applied. The two step approach gives us a new insight in partial least squares regression (PLS). Explicit maximum likelihood estimators of the variances and mean for the explanatory variables are derived. It is shown that the mean square error of the predictor in the two step model is always smaller than the one in PLS. Moreover, the two step model has been extended to handle grouped data. A real data set is analyzed to illustrate the performance of the two step approach and to compare it with other regularized methods.