Concentration and Model Selection Consistency of the Group Lasso for α$$ \alpha $$‐Mixing Errors

ABSTRACT

The group lasso in linear regression models is studied for ‐mixing subexponential errors. Nonasymptotic guarantees are provided for the estimation error of the sparse coefficient vector and the associated predictions for the high‐dimensional regime where the number of regressors can grow much faster than the sample size. Further, the group lasso is model selection consistent; that is, it picks the right variables with arbitrarily high probability. The results are applied to the index tracking problem in finance and illustrated by analysing stock data from the United States and Asia.