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Structural tests in additive regression

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  • Hardle, Wolfgang
  • Sperlich, Stefan
  • Spokoiny, Vladimir

Abstract

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.

Suggested Citation

  • Hardle, Wolfgang & Sperlich, Stefan & Spokoiny, Vladimir, 2000. "Structural tests in additive regression," DES - Working Papers. Statistics and Econometrics. WS 9863, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:9863
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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. 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.
    3. 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.
    4. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    5. 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.
    6. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    7. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    8. 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.
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    Cited by:

    1. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1286-1296, December.
    2. Donkers, Bas & Schafgans, Marcia M. A., 2005. "A method of moments estimator for semiparametric index models," LSE Research Online Documents on Economics 6815, London School of Economics and Political Science, LSE Library.
    3. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    4. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    5. Stefan Sperlich, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 419-427, September.
    6. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    7. Felix Abramovich & Italia Feis & Theofanis Sapatinas, 2009. "Optimal testing for additivity in multiple nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 691-714, September.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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    Keywords

    Additive models;

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