505 – Nonparametric Methods
A Note on Cumulative Mean Estimation
Bilin Zeng
California State University, Bakersfield
Zhou Yu
U.S. Census Bureau/University of Wisconsin-Madison
Xuerong Meggie Wen
Missouri University of Science & Technology
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.