Abstract

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. This work extensively investigated this idea and developed a new variable selection algorithm. The authors named this technique OLSAVS (Ordinary Least Squares After Variable Selection). The OLSAVS algorithm was implemented in R. Simulations were used to illustrate that the new method is able to produce better predictions with less bias for various error distributions. The OLSAVS method was compared with a few widely used shrinkage methods in terms of their achieved test root mean square error and bias.

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