Abstract

The quest for a good estimator of a certain focus or target is present regardless of the dimensionality of the data. Obtaining such a good estimator with low mean squared error (MSE), or a prediction with low prediction error often proceeds via a variable selection or model selection search. Estimators can also be averaged to enlarge the space of possible estimators in an attempt to further lower the MSE. While these methods are being studied mostly for unpenalized estimation methods in situations with the number of variables much smaller than the sample size, this article concentrates on the additional difficulties and challenges when applying focused model selection for squared error loss with penalized estimation, for example, in a context of high-dimensional data.