On the optimality of sliced inverse regression in high dimensions

Qian Lin, Xinran Li, Dongming Huang +1

The central subspace of a pair of random variables $(y,x)\in {\mathbb{R}}^{p+1}$ is the minimal subspace $\mathcal{S}$ such that $y\perp \perp x\mid P_{\mathcal{S}}x$…