The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 2 (1997), 577-612.
Nonlinear confounding in high-dimensional regression
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.
Ann. Statist., Volume 25, Number 2 (1997), 577-612.
First available in Project Euclid: 12 September 2002
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Adaptiveness dimension reduction graphics nonlinear regression overlinearization quasi-helical confounding information matrices regression diagnostics semi-parametrics sliced inverse regression
Li, Ker-Chau. Nonlinear confounding in high-dimensional regression. Ann. Statist. 25 (1997), no. 2, 577--612. doi:10.1214/aos/1031833665. https://projecteuclid.org/euclid.aos/1031833665