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Testing generalized linear and semiparametric models against smooth alternatives

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  • Göran Kauermann
  • Gerhard Tutz

Abstract

We propose goodness‐of‐fit tests for testing generalized linear models and semiparametric regression models against smooth alternatives. The focus is on models having both continous and factorial covariates. As a smooth extension of a parametric or semiparametric model we use generalized varying‐coefficient models as proposed by Hastie and Tibshirani. A likelihood ratio statistic is used for testing. Asymptotic expansions allow us to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping of the test statistic. The test is shown to have √n‐power, but in contrast with parametric tests it is powerful against smooth alternatives in general.

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  • Göran Kauermann & Gerhard Tutz, 2001. "Testing generalized linear and semiparametric models against smooth alternatives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 147-166.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:1:p:147-166
    DOI: 10.1111/1467-9868.00281
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    Cited by:

    1. Walter Krämer, 2020. "Interview mit Göran Kauermann," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 14(3), pages 305-312, December.
    2. Chin-Shang Li, 2016. "A test for the linearity of the nonparametric part of a semiparametric logistic regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 461-475, March.
    3. Maik Eisenbeiss & Goran Kauermann & Willi Semmler, 2007. "Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 503-522.
    4. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
    5. Göran Kauermann, 2006. "Nonparametric models and their estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 137-152, March.
    6. Kauermann, Göran, 2002. "On a Small Sample Adjustment for the Profile Score Function in Semiparametric Smoothing Models," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 471-485, August.

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