The raise estimator estimation, inference, and properties

Several methods using different approaches have been developed to remedy the consequences of collinearity. To the best of our knowledge, only the raise estimator proposed by García et al. (2010 García, C.B., García, J., Soto, J. (2010). The raise method: An alternative procedure to estimate the parameters in presence of collinearity. Qual. Quantity 45(2):403–423.[Crossref], [Web of Science ®] , [Google Scholar]) deals with this problem from a geometric perspective. This article fully develops the raise estimator for a model with two standardized explanatory variables. Inference in the raise estimator is examined, showing that it can be obtained from ordinary least squares methodology. In addition, contrary to what happens in ridge regression, the raise estimator maintains the coefficient of determination value constant. The expression of the variance inflation factor for the raise estimator is also presented. Finally, a comparative study of the raise and ridge estimators is carried out using an example.