A0871
Title: Sliced average variance estimation for tensor data
Authors: Chuanquan Li - Jiangxi University of Finance and Economics (China) [presenting]
Abstract: Tensor data have been widely used in many fields, e.g., modern biomedical imaging, chemometrics, and economics, but suffer from some common issues, such as high dimensional statistics. How to find their low-dimensional latent structure is of great interest. To this end, two efficient tensor-sufficient dimension reduction methods are developed based on the sliced average variance estimation (SAVE) to estimate the corresponding dimension reduction subspaces. The first one, entitled tensor sliced average variance estimation (TSAVE), works well when the response is discrete or takes finite values but is not $\sqrt{n}$ consistent for continuous response; the second one, named bias-correction tensor sliced average variance estimation (CTSAVE), is a de-biased version of the TSAVE method. The asymptotic properties of both methods are derived under mild conditions. Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.
