Ridge regression sampling properties and Monte Carlo experiment
The focus of this study is evaluate the asymptotic properties of ridge regression using a Monte Carlo simulation. In so doing, I will follow the work of Saleh and Kibria (1995), whose proposition is that when the design matrix is ill-conditioned, or multicollinear, preliminary test estimators combined with ridge regression methods are superior to the traditional estimators. By superior they mean that the mean square error (MSE) of the chosen ridge regression version is smaller than those of alternate estimators. They consider four versions of the OLS and compare their theoretical properties to those of the corresponding ridge regressions. The estimators are the following: unrestricted ridge regression estimator (URRE), restricted ridge regression estimator (RRRE), preliminary test ridge regression estimator (PTRRE), and shrinkage ridge regression estimator (SRRE). In order to evaluate the asymptotic properties of ridge regression, a Monte Carlo experiment was carried out. The idea was to approximate the parameters' values by generating random samples from the original model, and then averaging them. The quantities of interest were the median, mean, variance, and mean squared errors of the different versions for ordinary least squares and the corresponding versions of ridge regressions. The results from the Monte Carlo simulation were applied to solve the problem of multicollinearity arising when Feder's model was applied to the Dominican economy. Feder developed an analytical framework for the quantitative assessment of factor productivity differentials between exports and non-exports using aggregate data. The preliminary test ridge regression estimator performed better than the others estimators, as was suggested by Saleh and Kibria's analytical propositions. This is a very important breakthrough. The preliminary test ridge regression is a compromise estimator between the unrestricted and restricted ridge regression. Therefore, now it is feasible to combine sample and non-sample information in the process of automatically choosing a more efficient estimator.
Silverio, Pedro R, "Ridge regression sampling properties and Monte Carlo experiment" (1998). ETD Collection for Fordham University. AAI9825872.