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Component analysis for additive models

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  • Härdle, Wolfgang
  • Sperlich, Stefan
  • Spokoiny, Vladimir G.

Abstract

We consider the component analysis problem for a regression model with an additive structure. The problem is to check the hypothesis of linearity for each component without specifying the structure of the remaining components. In this paper we show that under mild conditions on the design and smoothness of the regression function, each component can be tested with the rate corresponding to the case if all the remaining components were known. The proposed procedure is based on the Haar transform and it is computationally straightforward.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb373:199752
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    References listed on IDEAS

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    1. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    2. Linton, O. B. & Härdle, Wolfgang, 1995. "Estimation of Additive Regression Models with Links," SFB 373 Discussion Papers 1995,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Lepski, O. V. & Spokoiny, V. G., 1995. "Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative," SFB 373 Discussion Papers 1995,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Lepski, V. & Spokoiny, V., 1995. "Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative," SFB 373 Discussion Papers 1995,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. 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.
    2. Hardle W. & Sperlich S. & Spokoiny V., 2001. "Structural Tests in Additive Regression," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1333-1347, December.
    3. 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.

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