Open Access
April 1997 Nonlinear confounding in high-dimensional regression
Ker-Chau Li
Ann. Statist. 25(2): 577-612 (April 1997). DOI: 10.1214/aos/1031833665


It is not uncommon to find nonlinear patterns in the scatterplots of regressor variables. But how such findings affect standard regression analysis remains largely unexplored. This article offers a theory on nonlinear confounding, a term for describing the situation where a certain nonlinear relationship in regressors leads to difficulties in modeling and related analysis of the data. The theory begins with a measure of nonlinearity between two regressor variables. It is then used to assess nonlinearity between any two projections from the high-dimensional regressor and a method of finding most nonlinear projections is given. Nonlinear confounding is addressed by taking a fresh new look at fundamental issues such as the validity of prediction and inference, diagnostics, regression surface approximation, model uncertainty and Fisher information loss.


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Ker-Chau Li. "Nonlinear confounding in high-dimensional regression." Ann. Statist. 25 (2) 577 - 612, April 1997.


Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0873.62071
MathSciNet: MR1439315
Digital Object Identifier: 10.1214/aos/1031833665

Primary: 62J20 , 62J99

Keywords: Adaptiveness , Dimension reduction , graphics , information matrices , Nonlinear regression , overlinearization , quasi-helical confounding , regression diagnostics , semi-parametrics , sliced inverse regression

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 2 • April 1997
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