Abstract
A new method for nonparametric regression data analysis by analyzing the sensitivity of normally large perturbations with the Principal Hessian Directions (PHD) method (Li 1992) is introduced, combining the merits of effective dimension reduction and visualization. We develop techniques for detecting perturbed points without knowledge of the functional form of the regression model when a small percentage of observations is subject to normally large values. The main feature in our proposed method is to estimate the deviation angle of the PHD direction. The basic idea is to recursively trim out perturbed points which cause larger directional deviations. Our multiple trimming method always reduces the pattern-ambiguity of geometric shape information about the regression surface. Several simulations with empirical results are reported.
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