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This article considers a linear model in a high dimensional data scenario. Wepropose a process which uses multiple loss functions both to select relevantpredictors and to estimate parameters, and study its asymptotic properties.Variable selection is conducted by a procedure called "vote", which aggregatesresults from penalized loss functions. Using multiple objective functionsseparately simplifies algorithms and allows parallel computing, which isconvenient and fast. As a special example we consider a quantile regressionmodel, which optimally combines multiple quantile levels. We show that theresulting estimators for the parameter vector are asymptotically efficient.Simulations and a data application confirm the three main advantages of ourapproach: (a) reducing the false discovery rate of variable selection; (b)improving the quality of parameter estimation; (c) increasing the efficiency ofcomputation.

Penalized regression with multiple loss functions and selection by vote