Adaptive group LASSO selection in quantile models
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The paper considers a linear model with grouped explanatory variables. If the model errors are not with zero mean and bounded variance or if model contains outliers, then the least squares framework is not appropriate. Thus, the quantile regression is an interesting alternative. In order to automatically select the relevant variable groups, we propose and study here the adaptive group LASSO quantile estimator. We establish the sparsity and asymptotic normality of the proposed estimator in two cases: fixed number and divergent number of variable groups. Numerical study by Monte Carlo simulations confirms the theoretical results and illustrates the performance of the proposed estimator.
KeywordsGroup selection Quantile model Adaptive LASSO Selection consistency Oracle properties
Mathematics Subject Classification62J05 62J07
The author sincerely thanks the Editor and two anonymous referees for their valuable comments which improved the quality of the paper.