A0519
Title: Sliced inverse regression with large structural dimensions
Authors: Dongming Huang - National University of Singapore (China) [presenting]
Songtao Tian - Tsinghua University (China)
Qian Lin - Tsinghua University (China)
Abstract: The central space of a joint distribution (X, Y) is the minimal subspace S such that Y and X are conditionally independent given PX, where P is the projection onto S. Sliced inverse regression (SIR), one of the most popular methods for estimating the central space, often performs poorly when the structural dimension d is large. It is demonstrated that the generalized signal-noise-ratio (gSNR) tends to be extremely small for a general multiple-index model when d is large. Then, the minimax rate for estimating the central space over a large class of high dimensional distributions with a large structural dimension d (i.e., there is no constant upper bound on d) is determined in the low gSNR regime. This result not only extends the existing minimax rate results for estimating the central space of distributions with fixed d to that with a large d, but also clarifies that the degradation in SIR performance is caused by the decay of signal strength. The technical tools developed might be of independent interest for studying other central space estimation methods.
