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Using thresholding difference-based estimators for variable selection in partial linear models

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  • Luo, June
  • Gerard, Patrick
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    Abstract

    A commonly used semiparametric model is considered. We adopt two difference based estimators of the linear component of the model and propose corresponding thresholding estimators that can be used for variable selection. For each thresholding estimator, variable selection in the linear component is developed and consistency of the variable selection procedure is shown. We evaluate our method in a simulation study and implement it on a real data set.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 12 ()
    Pages: 2601-2606

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2601-2606

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    Related research

    Keywords: Semi-parametric model; Differencing method; Asymptotic; High dimension; Variable selection;

    References

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    1. Debasri Mukherjee & Susan Pozo, 2011. "Exchange-rate volatility and trade: a semiparametric approach," Applied Economics, Taylor & Francis Journals, vol. 43(13), pages 1617-1627.
    2. Luo, June, 2012. "Asymptotic efficiency of ridge estimator in linear and semiparametric linear models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 58-62.
    3. G├╝lin Tabakan & Fikri Akdeniz, 2010. "Difference-based ridge estimator of parameters in partial linear model," Statistical Papers, Springer, vol. 51(2), pages 357-368, June.
    4. Du, Pang & Cheng, Guang & Liang, Hua, 2012. "Semiparametric regression models with additive nonparametric components and high dimensional parametric components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2006-2017.
    5. A. Yatchew, 2000. "Scale economies in electricity distribution: a semiparametric analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 187-210.
    6. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    7. Clifford Lam & Jianqing Fan, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    8. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    9. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    10. Huang, Jian & Wang, Deli & Zhang, Cun-Hui, 2005. "A Two-Way Semilinear Model for Normalization and Analysis of cDNA Microarray Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 814-829, September.
    11. Adonis Yatchew & Joungyeo Angela No, 2001. "Household Gasoline Demand in Canada," Econometrica, Econometric Society, vol. 69(6), pages 1697-1709, November.
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