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Error-in-Variables Jump Regression Using Local Clustering

Author

Listed:
  • Yicheng Kang
  • Xiaodong Gong
  • Jiti Gao
  • Peihua Qiu

Abstract

Error-in-variables regression is widely used in econometric models. The statistical analysis becomes challenging when the regression function is discontinuous and the distribution of measurement error is unknown. In this paper, we propose a novel jump-preserving curve estimation method. A major feature of our method is that it can remove the noise effectively while preserving the jumps well, without requiring much prior knowledge about the measurement error distribution. The jump-preserving property is achieved mainly by local clustering. We show that the proposed curve estimator is statistical consistent, and it performs favourably, in comparison with an existing jump-preserving estimator. Finally, we demonstrate our method by an application to a health tax policy study in Australia.

Suggested Citation

  • Yicheng Kang & Xiaodong Gong & Jiti Gao & Peihua Qiu, 2016. "Error-in-Variables Jump Regression Using Local Clustering," Monash Econometrics and Business Statistics Working Papers 13/16, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2016-13
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp13-16.pdf
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    References listed on IDEAS

    as
    1. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    2. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
    3. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    4. H.E. Frech Iii & Sandra Hopkins & Garry Macdonald, 2003. "The Australian Private Health Insurance Boom: Was It Subsidies Or Liberalised Regulation?," Economic Papers, The Economic Society of Australia, vol. 22(1), pages 58-64, March.
    5. Alfons Palangkaraya & Jongsay Yong, 2005. "Effects of Recent Carrot‐and‐Stick Policy Initiatives on Private Health Insurance Coverage in Australia," The Economic Record, The Economic Society of Australia, vol. 81(254), pages 262-272, September.
    6. Irene Gijbels & Peter Hall & Aloïs Kneip, 1999. "On the Estimation of Jump Points in Smooth Curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 231-251, June.
    7. Alfons Palangkaraya & Jongsay Yong & Elizabeth Webster & Peter Dawkins, 2009. "The income distributive implications of recent private health insurance policy reforms in Australia," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 10(2), pages 135-148, May.
    8. John Staudenmayer & David Ruppert, 2004. "Local polynomial regression and simulation–extrapolation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 17-30, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    clustering; demand for private health insurance; kernel smoothing; local regression; measurement errors; price elasticity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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