B0475
Title: Robust adaptive variable selection in ultra-high dimensional linear regression models
Authors: Abhik Ghosh - Indian Statistical Institute (India) [presenting]
Maria Jaenada - Universidad Complutense Madrid (Spain)
Leandro Pardo - Universidad Complutense Madrid (Spain)
Abstract: The focus is on the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property along with an easier computational burden. However, the usual adaptive procedures (e.g., adaptive LASSO) based on the squared error loss function are extremely non-robust in the presence of data contamination. We present a regularization procedure for the ultra-high dimensional data using a robust loss function based on the popular density power divergence (DPD) measure along with the adaptive LASSO penalty. We theoretically study the robustness and the large-sample properties of the proposed adaptive robust estimators for a general class of error distributions; in particular, we show that the proposed adaptive DPD-LASSO estimator is highly robust, satisfies the oracle variable selection property, and the corresponding estimators of the regression coefficients are consistent and asymptotically normal under easily verifiable set of assumptions. Numerical illustrations are provided for the mostly used normal error density. Finally, the proposal is applied to analyze an interesting spectral dataset in the field of chemometrics.
