Olsavs: A New Algorithm For Model Selection

The shrinkage methods such as Lasso and Relaxed Lasso introduce some bias in order to reduce the variance of the regression coefficients in multiple linear regression models. One way to reduce bias after shrinkage of the coefficients would be to apply ordinary least squares to the subset of predictors selected by the shrinkage method used. We extensively studied this idea in this work and developed a new variable selection algorithm. We named this technique OLSAVS (Ordinary Least Squares After Variable Selection). We have implemented the OLSAVS algorithms in R. Simulations were used to illustrate that the new method is able to produce better predictions with less bias for various error distributions. We compare the OLSAVS method with a few widely used shrinkage methods in terms of their achieved test root mean square error and bias.