A0221
Title: Inference for the dimension of a regression relationship using pseudo-covariates
Authors: Shih-Hao Huang - National Central University (Taiwan) [presenting]
Kerby Shedden - Statistics (United States)
Hsin-wen Chang - Academia Sinica (Taiwan)
Abstract: The main goal of data analysis using dimension reduction methods is to summarize how the response is related to the covariates through a few linear combinations. One key issue is determining the minimal number of relevant covariate combinations, which is the dimension of the sufficient dimension reduction (SDR) subspace. The purpose is to propose an easily-applied approach to conduct inference for the dimension of the SDR subspace based on augmentation of the covariate set with simulated pseudo-covariates. Applying the partitioning principle to the possible dimensions, rigorous sequential testing is used to select the dimensionality by comparing the strength of the signal arising from the actual covariates to that appearing to arise from the pseudo-covariates. It is shown that under a "uniform direction" condition, this approach can be used in conjunction with several popular SDR methods, including sliced inverse regression. In these settings, the test statistic asymptotically follows a beta distribution and therefore is easily calibrated. Moreover, the sequential testing's family-wise type I error rate is rigorously controlled. Simulation studies and an analysis of newborn anthropometric data demonstrate the robustness of the proposed approach and indicate that the power is comparable to or greater than the alternatives.
