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We consider the application of a popular penalised regression method, RidgeRegression, to data with very high dimensions and many more covariates thanobservations. Our motivation is the problem of out-of-sample prediction and thesetting is high-density genotype data from a genome-wide association orresequencing study. Ridge regression has previously been shown to offerimproved performance for prediction when compared with other penalisedregression methods. One problem with ridge regression is the choice of anappropriate parameter for controlling the amount of shrinkage of thecoefficient estimates. Here we propose a method for choosing the ridgeparameter based on controlling the variance of the predicted observations inthe model.  Using simulated data, we demonstrate that our method outperforms subsetselection based on univariate tests of association and another penalisedregression method, HyperLasso regression, in terms of improved predictionerror. We extend our approach to regression problems when the outcomes arebinary (representing cases and controls, as is typically the setting forgenome-wide association studies) and demonstrate the method on a real dataexample consisting of case-control and genotype data on Bipolar Disorder, takenfrom the Wellcome Trust Case Control Consortium and the Genetic AssociationInformation Network.

A semi-automatic method to guide the choice of ridge parameter in ridge regression