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Oracally Efficient Two-Step Estimation of Generalized Additive Model

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  • Rong Liu
  • Lijian Yang
  • Wolfgang K. Härdle

Abstract

The generalized additive model (GAM) is a multivariate nonparametric regression tool for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions and the constant, which are oracally efficient under weak dependence. The SBK technique is both computationally expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Inference can be made on component functions based on asymptotic normality. Simulation evidence strongly corroborates the asymptotic theory. The method is applied to estimate insolvent probability and to obtain higher accuracy ratio than a previous study. Supplementary materials for this article are available online.

Suggested Citation

  • Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:619-631
    DOI: 10.1080/01621459.2013.763726
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    References listed on IDEAS

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    1. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.
    2. Lan Xue & Hua Liang, 2010. "Polynomial Spline Estimation for a Generalized Additive Coefficient Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 26-46, March.
    3. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
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    More about this item

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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