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Oracle-Efficient Nonparametric Estimation Of An Additive Model With An Unknown Link Function

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  • Horowitz, Joel L.
  • Mammen, Enno

Abstract

This paper describes an estimator of the additive components of a nonparametric additive model with an unknown link function. When the additive components and link function are twice differentiable with sufficiently smooth second derivatives, the estimator is asymptotically normally distributed with a rate of convergence in probability of n−2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, the estimator has no curse of dimensionality. Moreover, the asymptotic distribution of the estimator of each additive component is the same as it would be if the link function and the other components were known with certainty. Thus, asymptotically there is no penalty for not knowing the link function or the other components.

Suggested Citation

  • Horowitz, Joel L. & Mammen, Enno, 2011. "Oracle-Efficient Nonparametric Estimation Of An Additive Model With An Unknown Link Function," Econometric Theory, Cambridge University Press, vol. 27(3), pages 582-608, June.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:03:p:582-608_00
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    Citations

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    Cited by:

    1. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers CWP20/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Orazio Attanasio & Elena Pastorino, 2020. "Nonlinear Pricing in Village Economies," Econometrica, Econometric Society, vol. 88(1), pages 207-263, January.
    3. Shujie Ma & Oliver Linton & Jiti Gao, 2017. "Estimation and inference in semiparametric quantile factor models," Monash Econometrics and Business Statistics Working Papers 8/17, Monash University, Department of Econometrics and Business Statistics.
    4. Lewbel, Arthur & Lu, Xun & Su, Liangjun, 2015. "Specification testing for transformation models with an application to generalized accelerated failure-time models," Journal of Econometrics, Elsevier, vol. 184(1), pages 81-96.
    5. Shujie Ma & Oliver Linton & Jiti Gao, 2018. "Estimation in semiparametric quantile factor models," CeMMAP working papers CWP07/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers 20/12, Institute for Fiscal Studies.
    7. Wu, Frank C.Z., 2024. "A high-dimensional additive nonparametric model," Journal of Economic Dynamics and Control, Elsevier, vol. 166(C).
    8. Ma, Shujie & Linton, Oliver & Gao, Jiti, 2021. "Estimation and inference in semiparametric quantile factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 295-323.

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