B0180
Title: Semiparametrically efficient method for enveloped central space
Authors: Linquan Ma - University of Wisconsin-Madison (United States)
Jixin Wang - Rice University (United States) [presenting]
Han Chen - University of California at Davis (United States)
Lan Liu - University of Minnesota at Twin Cites (United States)
Abstract: The estimation of the central space is at the core of the sufficient dimension reduction (SDR) literature. However, it is well known that the finite-sample estimation suffers from collinearity among predictors. The predictor envelope method under linear models can alleviate the problem by targeting a bigger space which not only envelopes the central information but also partitions the predictors by finding an uncorrelated set of material and immaterial predictors. One limitation of the predictor envelope is that it has strong distributional and modelling assumptions and therefore, it cannot be readily used in semiparametric settings where SDR usually nests. The envelope model is generalized by defining the enveloped central space and proposing a semiparametric method to estimate it. The entire class of regular and asymptotically linear (RAL) estimators are derived as well as the locally and globally semiparametrically efficient estimators for the enveloped central space. Based on the connection between the predictor envelope and partial least squares (PLS), the methods can also be used to calculate the PLS space beyond linearity. In the simulations, the methods are shown to be both robust and accurate for estimating the enveloped central space under different settings.
