Yanyuan Ma, Liping Zhu
Department of Statistics, Texas A&M University, College Station Texas 77843, U.S.A
Biometrika. 2013 Jun;100(2):371-383. doi: 10.1093/biomet/ass075.
Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation.
在充分降维的背景下，通常假定线性（有时与恒定方差一起）。众所周知，当这些条件不成立时，盲目使用它们可能会导致在估计中心子空间和中心均值子空间时出现不一致。令人惊讶的是，我们发现即使这些条件成立，使用它们也会带来效率损失。这种矛盾的现象通过切片逆回归和主Hessian方向得到了说明。效率损失也适用于其他降维方法。我们通过理论研究解释了这一实证发现。
