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Semiparametric penalty function method in partially linear model selection

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  • Dong, Chaohua
  • Gao, Jiti
  • Tong, Howell

Abstract

Model selection in nonparametric and semiparametric regression is of both theoretical and practical interest. Gao and Tong (2004) proposed a semiparametric leave–more–out cross–validation selection procedure for the choice of both the parametric and nonparametric regressors in a nonlinear time series regression model. As recognized by the authors, the implementation of the proposed procedure requires the availability of relatively large sample sizes. In order to address the model selection problem with small or medium sample sizes, we propose a model selection procedure for practical use. By extending the so–called penalty function method proposed in Zheng and Loh (1995, 1997) through the incorporation of features of the leave-one-out cross-validation approach, we develop a semiparametric, consistent selection procedure suitable for the choice of optimum subsets in a partially linear model. The newly proposed method is implemented using the full set of data, and simulations show that it works well for both small and medium sample sizes.

Suggested Citation

  • Dong, Chaohua & Gao, Jiti & Tong, Howell, 2006. "Semiparametric penalty function method in partially linear model selection," MPRA Paper 11975, University Library of Munich, Germany, revised Aug 2006.
    • Handle: RePEc:pra:mprapa:11975
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    References listed on IDEAS

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    1. Hardle, W. & Hall, P. & Marron, J., 1990. "Regression smoothing parameters that are not far from their optimum," LIDAM Discussion Papers CORE 1990009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Yao, Qiwei & Tong, Howell, 1994. "On subset selection in non-parametric stochastic regression," LSE Research Online Documents on Economics 6409, London School of Economics and Political Science, LSE Library.
    3. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    4. Vieu, Philippe, 1994. "Choice of regressors in nonparametric estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(5), pages 575-594, June.
    5. Jiti Gao & Howell Tong, 2004. "Semiparametric non‐linear time series model selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 321-336, May.
    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
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    Cited by:

    1. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.

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    More about this item

    Keywords

    Linear model; model selection; nonparametric method; partially linear model; semiparametric method;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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