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Group selection via adjusted weighted least absolute deviation regression. (English) Zbl 1439.62167

Summary: In applications, predictors are naturally grouped with some variables in nonzero groups being irrelevant, simultaneously variable selection at both the group and within-group levels is more desirable. In addition, to achieve a robust estimation against outliers in both covariates and responses, combining the excellent properties of weighted least absolute deviation (WLAD) and least squares, we propose an adjusted WLAD (AWLAD) regression estimator with the adaptive group bridge penalty. Importantly, we demonstrate that the AWLAD estimator enjoys the oracle property when the number of parameters grows with the sample size. Simulation studies and a real data analysis indicate that the AWLAD has superior performance in the finite sample cases.

MSC:

62J05 Linear regression; mixed models
62F12 Asymptotic properties of parametric estimators
62J07 Ridge regression; shrinkage estimators (Lasso)
62F07 Statistical ranking and selection procedures
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