A consistent estimator for the supremum of the projection index based on sliced inverse regression

Abstract

To seek the nonlinear structure hidden in data points of high-dimension, a transformation related to projection pursuit method and a projection index were proposed by Li (1989, 1990 ). In this paper, we present a consistent estimator of the supremum of the projection index based sliced inverse regression technique. This estimator also suggests a method to obtain approximately the most interesting projection in the general case.

Keywords:

• Sliced inverse regression
• Projection index
• Consistent estimator
• Empirical processes