A study of sensitivity analysis on the method of principal Hessian directions
type: Item
instance of: scholarly article
title: A study of sensitivity analysis on the method of principal Hessian directions
zbMATH Open document ID: 1007.62055
author: Lue Heng-Hui
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
review text: A nonlinear dimension reduction problem is considered with data described by the model \(y_j=g(\beta'_1x_j,\dots,\beta_k'x_j,\varepsilon_j)\), where \((y_j,x_j)_{j=1}^n\) are observations, \(g:R^k\to R\) is an unknown function, \(\beta_i\) are unknown and should be estimated, and \(\varepsilon_j\) is a random error. The principal Hessian directions (PHD) technique is described for estimation of the \(\beta_j\). Then the case is considered where \(k=2\), \(\varepsilon_j\) are absent, but \(y\) and \(x\) can be perturbed at some points by an additive Gaussian noise. For this case the asymptotic distribution of the angle between the perturbed and non-perturbed PHD is described. Results of simulations and analysis of base ball data are presented.
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62-07
zbMATH DE Number: 1878602
zbMATH Keywords: dimension reduction
zbMATH Keywords: nonlinear principal components
zbMATH Keywords: perturbation
MaRDI profile type: Publication
full work available at URL: s001800100054
OpenAlex ID: W3939841
cites work: Q4839364
cites work: Q4844382
cites work: Principal Hessian Directions Revisited
cites work: Slicing regression: A link-free regression method
cites work: A Systematic Approach to the Analysis of Complex Interaction Patterns in Two-Level Factorial Designs
cites work: On almost linearity of low dimensional projections from high dimensional data
cites work: An asymptotic theory for sliced inverse regression
cites work: Q4109608
cites work: Sliced Inverse Regression for Dimension Reduction
cites work: On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma
cites work: Interactive Tree-Structured Regression via Principal Hessian Directions
cites work: Q3790486
cites work: Q3999500
DOI: 10.1007/S001800100054
description: scientific article; zbMATH DE number 1878602