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A Note On Least Absolute Deviation Estimation Of A Threshold Model

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  • Caner, Mehmet

Abstract

This paper develops the limit law for the least absolute deviation estimator of the threshold parameter in linear regression. In this respect, we extend the literature of threshold models. The existing literature considers only the least squares estimation of the threshold parameter (see Chan, 1993, Annals of Statistics 21, 520–533; Hansen, 2000, Econometrica 68, 575–605). This result is useful because in the case of heavy-tailed errors there is an efficiency loss resulting from the use of least squares. Also, for the first time in the literature, we derive the limit law for the likelihood ratio test for the threshold parameter using the least absolute deviation technique.

Suggested Citation

  • Caner, Mehmet, 2002. "A Note On Least Absolute Deviation Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 18(3), pages 800-814, June.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:03:p:800-814_18
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    Citations

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    Cited by:

    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Correa, Arnildo da Silva & Minella, André, 2010. "Nonlinear mechanisms of the exchange rate pass-through: A Phillips curve model with threshold for Brazil," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 64(3), September.
    3. Chung-Ming Kuan & Christos Michalopoulos & Zhijie Xiao, 2017. "Quantile Regression on Quantile Ranges – A Threshold Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 99-119, January.
    4. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    5. Kato, Kengo, 2009. "Asymptotics for argmin processes: Convexity arguments," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1816-1829, September.
    6. Junho Lee & Ying Sun & Huixia Judy Wang, 2021. "Spatial cluster detection with threshold quantile regression," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    7. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    8. Antonio F. Galvao Jr. & Gabriel Montes‐Rojas & Jose Olmo, 2011. "Threshold quantile autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 253-267, May.
    9. Neil Foster-McGregor & Anders Isaksson & Florian Kaulich, 2013. "Importing, Productivity and Absorptive Capacity in Sub-Saharan African Manufacturing Firms," wiiw Working Papers 105, The Vienna Institute for International Economic Studies, wiiw.
    10. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.
    11. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    12. Chris Papageorgiou & Shankha Chakraborty, 2005. "Diseases and Development," Departmental Working Papers 2005-12, Department of Economics, Louisiana State University.

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