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Activity Number: 505
Type: Contributed
Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #311375
Title: A Note on Cumulative Mean Estimation
Author(s): Bilin Zeng*+ and Zhou Yu and Xuerong Wen
Companies: California State University, Bakersfield and U.S. Census Bureau/University of Wisconsin-Madison and Missouri University of Science & Technology
Keywords: Dimension Reduction ; Cumulative Slicing Estimation ; Intraslice Covariance Estimatation ; Sliced Inverse Regression
Abstract:

For many-valued or continuous Y , the standard practice in sufficient dimension reduction (Li, 1991; Cook, 1998) of replacing the response Y with a discrete version of Y usually results in the loss of power due to the loss of the intra-slice information. Most of the existing slicing methods highly rely on the choices of the total number of slices h. Zhu et al. (2010) proposed a method called the cumulative slicing estimation (CUME) which avoids the otherwise subjective selection of h. In this paper, we revisit CUME from a different perspective to gain more insights, and then refine its performance by incorporating the intra-slice covariances. We prove that our new method, which we call the covariance cumulative slicing estimation(COCUM), is more comprehensive than CUME since it captures a larger part of the central subspace. Simulation studies suggest that our method is comparable to CUME, and outperforms CUME when the response is skewed. The asymptotic results of COCUM are also well proved.


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