Nonlinear confounding in high-dimensional regression

• 成果类型: Article
• 署名作者: Li, KC
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 577-612
• 关键词: sliced inverse regression; Projection Pursuit Regression; MULTIPLE-REGRESSION; data visualization; reduction; models; link; plots

摘要

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.