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Abstract:
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In sufficient dimension reduction area, slicing estimation based methods are promising in recovery of the central subspace. However, the asymptotic properties and efficacy of the slicing estimation for many inverse regression methods depends heavily upon the choice of slice number when the response variable is continuous. How to select slice number is a longstanding, and still open problem. In this paper, we propose a discretization-expectation (DEE) method. Following the idea of slicing estimation though, DEE completely avoids selecting the number of slices, and meanwhile preserves the integrity of the original central subspace. This generic method assures the asymptotic normality of slicing estimators, and can be applied to multivariate response cases. Finally, DEE is compared with existing estimators by extensive simulations and an illustrative real data example.
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