Are you aware of any regularized regression methods (i.e. Lasso, elastic net) which allows for using cases with incomplete (missing) data (e.g. using EM estimation)? And if yes, is the method available in some software, such as R or MATLAB?

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    $\begingroup$ If you're using R anyway, you might as well just use any of the dozens of imputation tools prior to conducting your analysis. $\endgroup$ – Sycorax Mar 16 '15 at 14:32
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    $\begingroup$ Seems rather unlikely; the problems are completely distinct. However, for R you'll find both missing data software, e.g. multiple imputation, and regularization tools aplenty. Just use the one, then the other. $\endgroup$ – conjugateprior Mar 16 '15 at 14:33
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    $\begingroup$ Thanks but how would you combine several imputed datasets into one which properly reflect the uncertainty due to missing values. Rubin's rule seem not appropriate because we cannot really us the standard errors of biased coefficient and I cannot see how to assess prediction accuracy using mi and cross-validation methods. All other imputation methods seem to ignore this problematic $\endgroup$ – Stats_Monkey Mar 16 '15 at 14:40

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