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Structural Tests in Additive Regression

  • Hardle W.
  • Sperlich S.
  • Spokoiny V.

We consider the component analysis problem for a regression model with an additive structure. The problem is to test if some of the additive components is 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 presented method 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 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 good performance of the test.

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Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 96 (2001)
Issue (Month): (December)
Pages: 1333-1347

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Handle: RePEc:bes:jnlasa:v:96:y:2001:m:december:p:1333-1347
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  1. Richard Blundell & Alan Duncan & Costas Meghir, 1998. "Estimating Labor Supply Responses Using Tax Reforms," Econometrica, Econometric Society, vol. 66(4), pages 827-862, July.
  2. Härdle, Wolfgang & Sperlich, Stefan & Spokoiny, Vladimir G., 1997. "Component analysis for additive models," SFB 373 Discussion Papers 1997,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  4. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Working Papers 99-02, University of Iowa, Department of Economics.
  5. Thomas Mroz, . "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," University of Chicago - Population Research Center 84-8, Chicago - Population Research Center.
  6. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, November.
  7. Spokoiny, Vladimir G., 1999. "Variance estimation for high-dimensional regression models," SFB 373 Discussion Papers 1999,86, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An adaptive, rate-optimal test of a parametric model against a nonparametric alternative," SFB 373 Discussion Papers 1999,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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