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Non‐parametric Regression Tests Using Dimension Reduction Techniques

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  • BERTHOLD R. HAAG

Abstract

. Testing for parametric structure is an important issue in non‐parametric regression analysis. A standard approach is to measure the distance between a parametric and a non‐parametric fit with a squared deviation measure. These tests inherit the curse of dimensionality from the non‐parametric estimator. This results in a loss of power in finite samples and against local alternatives. This article proposes to circumvent the curse of dimensionality by projecting the residuals under the null hypothesis onto the space of additive functions. To estimate this projection, the smooth backfitting estimator is used. The asymptotic behaviour of the test statistic is derived and the consistency of a wild bootstrap procedure is established. The finite sample properties are investigated in a simulation study.

Suggested Citation

  • Berthold R. Haag, 2008. "Non‐parametric Regression Tests Using Dimension Reduction Techniques," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 719-738, December.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:4:p:719-738
    DOI: 10.1111/j.1467-9469.2008.00608.x
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    References listed on IDEAS

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    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
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    5. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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    7. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    8. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
    9. Norbert Christopeit & Stefan G. N. Hoderlein, 2006. "Local Partitioned Regression," Econometrica, Econometric Society, vol. 74(3), pages 787-817, May.
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    Cited by:

    1. Fengler, Matthias R. & Mammen, Enno & Vogt, Michael, 2013. "Additive modeling of realized variance: tests for parametric specifications and structural breaks," Economics Working Paper Series 1332, University of St. Gallen, School of Economics and Political Science.
    2. Mammen, Enno & Park, Byeong U. & Schienle, Melanie, 2012. "Additive models: Extensions and related models," SFB 649 Discussion Papers 2012-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Fengler, M.R. & Mammen, E. & Vogt, M., 2015. "Specification and structural break tests for additive models with applications to realized variance data," Journal of Econometrics, Elsevier, vol. 188(1), pages 196-218.
    4. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    5. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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