It is well known that Ordinary Least Squares (OLS) results in the best linear unbiased estimator for the parameters in a linear model. However, when the predictors are highly correlated, the OLS estimator may not perform well in terms of mean squared error. Further, when the number of predictors exceeds the sample size, the OLS estimator is not uniquely defined. In this talk, we introduce a new objective function and corresponding estimator, called Complete Least Squares, as an alternative to OLS. We establish a connection between this new estimator and the well-known ridge regression estimator, and we motivate the use of Complete Least Squares for the variable screening problem - reducing the pool of potential covariates when the number of predictors exceeds the sample size.
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