Structural tests in additive regression

• 成果类型: Article; Proceedings Paper
• 署名作者: Härdle, W; Sperlich, S; Spokoiny, V
• 署名单位: Humboldt University of Berlin; Universidad Carlos III de Madrid
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214501753382264
• 发表日期: 2001
• 页码: 1333-1347
• 关键词: data-driven version; Goodness-of-fit; variance; MODEL; signal

摘要

We consider the component analysis problem for a regression model with an additive structure. The problem is to test whether some of the additive components are of polynomial structure (e.g., linear) without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The method that we present is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the design and smoothness of the regression function. The results demonstrate that each component of the model can be tested with the rate corresponding to the case if all of the remaining components were known, The proposed procedure is also computationally straightforward. Simulation results and a real data example about female labor Supply demonstrate the test's good performance.