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Local Likelihood Estimation in Generalized Additive Models

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  • Göran Kauermann
  • J. D. Opsomer

Abstract

ABSTRACT. Generalized additive models are a popular class of multivariate non‐parametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are poorly understood. In this article, we propose a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator fitted by local polynomial regression. We derive the statistical properties of the estimator and show that it achieves the same asymptotic convergence rate as a one‐dimensional local polynomial regression estimator. We also propose a wild bootstrap estimator for calculating point‐wise confidence intervals for the additive component functions. The practical behaviour of the proposed estimator is illustrated through a simulation experiment.

Suggested Citation

  • Göran Kauermann & J. D. Opsomer, 2003. "Local Likelihood Estimation in Generalized Additive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 317-337, June.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:317-337
    DOI: 10.1111/1467-9469.00333
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    Cited by:

    1. 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.
    2. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    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. Daniel O. Scharfstein & Rafael A. Irizarry, 2003. "Generalized Additive Selection Models for the Analysis of Studies with Potentially Nonignorable Missing Outcome Data," Biometrics, The International Biometric Society, vol. 59(3), pages 601-613, September.

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