B0472
Title: Adaptive regression selection and estimation under sparse $\ell_q$-constraints
Authors: Yuhong Yang - University of Minnesota (United States)
Frank Gao - University of Idaho (United States)
Zang Wang - University of Minnesota (United States)
Sandra Paterlini - European Business School Germany (Germany) [presenting]
Abstract: Considering fixed design linear regression settings, the aim is to construct an estimator that target the best performance among all the linear combinations of the predictors under a sparse $\ell_q$-pseudonorm ($0\le q \le 1$) constraint on the linear coefficients. Our strategy is to choose a model using the model selection criterion ABC' for the case of unknown variance, and the resulting least squares estimators are used for the beta coefficients. Although our estimator does not directly consider the $\ell_q$-constraint, we show that it automatically adapts to the sparsity of the regression function in terms of $\ell_q$-representation and achieve the minimax rate. By relying on heuristics, we introduce a new algorithm for optimal ABC' model selection and estimation. Comparisons on simulated data with state-of-art methods, including Lasso and non-convex penalties, show remarkable properties in terms of model selection, estimation error and mean squared error. Finally, by applying it to financial data, we point out its practical use in developing effective investment strategies.
