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Infinite Order Cross-Validated Local Polynomial Regression

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  • Peter G. Hall
  • Jeffrey S. Racine

Abstract

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determination of the polynomial order may not be optimal in general, while the joint determination of the polynomial order and bandwidth presents some interesting theoretical and practical challenges. In this paper we propose a data-driven approach towards the joint determination of the polynomial order and bandwidth, provide theoretical underpinnings, and demonstrate that improvements in both finite-sample efficiency and rates of convergence can thereby be obtained. In the case where the true data generating process (DGP) is in fact a polynomial whose order does not depend on the sample size, our method is capable of attaining the √n rate often associated with correctly specified parametric models, while the estimator is shown to be uniformly consistent for a much larger class of DGPs. Theoretical underpinnings are provided,finite-sample properties are examined, and an application highlights finite-sample improvements arising from the use of the proposed method.

Suggested Citation

  • Peter G. Hall & Jeffrey S. Racine, 2013. "Infinite Order Cross-Validated Local Polynomial Regression," Department of Economics Working Papers 2013-05, McMaster University.
  • Handle: RePEc:mcm:deptwp:2013-05
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2013-05.pdf
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    Cited by:

    1. Jean Pierre Huiban & Camilla Mastromarco & Antonio Musolesi & Michel Simioni, 2016. "The impact of pollution abatement investments on production technology: new insights from frontier analysis," SEEDS Working Papers 0716, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jul 2016.
    2. Nadine McCloud & Christopher F. Parmeter, 2017. "Calculating Degrees of Freedom in Multivariate Local Polynomial Regression," Working Papers 2017-14, University of Miami, Department of Economics.
    3. Michael Delgado & Christopher Parmeter & Valentina Hartarska & Roy Mersland, 2015. "Should all microfinance institutions mobilize microsavings? Evidence from economies of scope," Empirical Economics, Springer, vol. 48(1), pages 193-225, February.
    4. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, Open Access Journal, vol. 1(2), pages 1-23, September.
    5. repec:eee:econom:v:201:y:2017:i:1:p:1-18 is not listed on IDEAS
    6. Subal Kumbhakar & Christopher Parmeter, 2015. "Introduction," Empirical Economics, Springer, vol. 48(1), pages 1-8, February.

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    Keywords

    model selection; efficiency; rates of convergence;

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