Structural tests in additive regression

Wolfgang Härdle, Stefan Sperlich, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1333-1347
Number of pages15
JournalJournal of the American Statistical Association
Issue number456
Publication statusPublished - 1 Dec 2001
Externally publishedYes


  • Additive model
  • Component analysis
  • Haar basis
  • Hypothesis testing
  • Nonparametric alternative
  • Regression


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