An Adaptive Estimation of Dimension Reduction Space

Summary Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters (than for that of the nonparametric function). In contrast, a faster consistency rate can be achieved by the MAVE method even without undersmoothing the nonparametric link function estimator. The…

• WT
  Wellcome Trust
• LS
  London School of Economics and Political Science
• UO
  University of Hong Kong
• EA
  Engineering and Physical Sciences Research Council
• BA
  Biotechnology and Biological Sciences Research Council