We survey and apply several techniques from the statistical and computer science literature to the problem of demand estimation. To improve out-of-sample prediction accuracy, we propose a method of combining the underlying models via linear regression. Our method is robust to a large number of regressors; scales easily to very large data sets; combines model selection and estimation; and can flexibly approximate arbitrary non-linear functions. We illustrate our method using a standard scanner panel data set and find that our estimates are considerably more accurate in out-of-sample predictions of demand than some commonly used alternatives.