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Oracally efficient two-step estimation of generalized additive model

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Listed:
  • Liu, Rong
  • Yang, Lijian
  • Härdle, Wolfgang Karl

Abstract

Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions. Our results are for weakly dependent data and we prove oracle efficiency. The SBK techniques is both computational 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 with the asymptotic theory.

Suggested Citation

  • Liu, Rong & Yang, Lijian & Härdle, Wolfgang Karl, 2011. "Oracally efficient two-step estimation of generalized additive model," SFB 649 Discussion Papers 2011-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-016
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    References listed on IDEAS

    as
    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

    Keywords

    bandwidths; B spline; knots; link function; mixing; Nadaraya-Watson estimator;
    All these keywords.

    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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