| For regression analysis with multicollinear data, we consider ridge regression and principal components regression as alternatives to the least squares regression. When the ridge factor has to be estimated from the data, we discuss the choice of asymptotic ridge factor and the asymptotic distribution of several ridge factors. The mean squared errors of operational ridge regression estimators are evaluated asymptotically. We consider a "modified" principal components regression and study its properties. Some guidelines are set up for regression analysis of multicollinear data: what regression procedure is the best for the data?;The ridge-type and the principal components approaches are studied in related other areas such as canonical correlation analysis, particularly when the data shows multicollinearity. |
