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Title: The central mean envelope for dimension reduction Authors:  Xin Zhang - Florida State University (United States)
Chung Eun Lee - University of Tennessee, Knoxville (United States) [presenting]
Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States)
Abstract: A new envelope model, called central mean envelope, is introduced which generalizes a previous envelope model in two aspects. One aspect is that the central mean envelope does not impose a linear mean structure which can be viewed as a model-free method. Furthermore, the central mean envelope can have a heteroscedastic error to reduce the dimension. In particular, we seek a minimum subspace that reduces the conditional variance matrix of $Y$ given $X$ and fully captures the conditional mean dependence between $Y$ and $X$. To estimate the central mean envelope, we use the martingale difference divergence matrix (MDDM) which measures the conditional mean dependence. Moreover, if there exists the heteroscedasticity, we use the slicing method or $k$-means method to find the subspace that reduces the conditional variance matrix. Theory is also provided regarding the consistency of the projection matrix associated with the central mean envelope. Favorable finite sample performance is demonstrated via simulations in comparison with some existing methods.