A0934
Title: Enveloped Huber regression
Authors: Le Zhou - Hong Kong Baptist University (Hong Kong) [presenting]
Dennis Cook - University of Minnesota (United States)
Hui Zou - University of Minnesota (United States)
Abstract: Huber regression (HR) is a popular flexible alternative to the least squares regression when the error follows a heavy-tailed distribution. A new method called the enveloped Huber regression (EHR) is proposed by considering the envelope assumption that some subspace of the predictors exist that have no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part. Different from the envelope least squares (ENV) model, whose estimation is based on maximum normal likelihood, the estimation of the EHR model is through the generalized method of moments. The asymptotic normality of the EHR estimator is established, and it is shown that EHR is more efficient than HR. Moreover, EHR is more efficient than ENV when the error distribution is heavy-tailed while maintaining a small efficiency loss when the error distribution is normal. Moreover, the theory also covers the heteroscedastic case in which the error may depend on the covariates. The envelope dimension in EHR is a tuning parameter that is determined by the data in practice. A novel generalized information criterion (GIC) is further proposed for dimension selection and its consistency is established. Extensive numerical studies confirm the messages of the theory.
