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Title: A general framework for sparse sufficient dimension reduction Authors:  Wei Luo - Zhejiang University (China) [presenting]
Abstract: Sparse sufficient dimension reduction incorporates the sparsity assumption in variable selection into sufficient dimension reduction (SDR), and improves the latter in both the interpretability and the estimation accuracy. We construct a general framework to modify the ordinary SDR methods into sparse SDR methods, based on the recent serial work on uniform semiparametric SDR methods. The motivation comes from the observation that the minimum average variance estimator (MAVE) and the semiparametrically efficient estimator for the central mean subspace are asymptotically equivalent when the data are homoscedastic for regression, the justification of which makes independent contribution to the SDR literature. We show that, under certain regularity conditions, the sparse SDR methods based on the proposed framework have the variable selection consistency and the asymptotic normality, and enjoy a weak oracle property. In high-dimensional cases, we justify the asymptotic consistency of the proposed sparse sliced inverse regression. From simulation studies, the proposed sparse SDR methods have superior performance than the comparable existing sparse SDR methods.