On the Optimality of Sliced Inverse Regression in High

Abstract

By Qian Lin‡∗ Xinran Li‡∗ Dongming Huang‡∗ and Jun S. Liu‡∗ Harvard University‡ The central subspace of a pair of random variables (y,x) ∈ R is the minimal subspace S such that y ⊥ x|PSx. In this paper, we consider the minimax rate of estimating the central space of the multiple index models y = f(βτ1x,β τ 2x, ...,β τ dx, ) with at most s active predictors… (More)

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