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Threshold Regression with Nonparametric Sample Splitting

Author

Listed:
  • Yoonseok Lee
  • Yulong Wang

Abstract

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. Our model has broad empirical relevance as illustrated by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery. We find that the new empirical results are substantially different from those in the existing studies.

Suggested Citation

  • Yoonseok Lee & Yulong Wang, 2019. "Threshold Regression with Nonparametric Sample Splitting," Papers 1905.13140, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:1905.13140
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    Cited by:

    1. Yoonseok Lee & Yulong Wang, 2020. "Inference in Threshold Models," Center for Policy Research Working Papers 223, Center for Policy Research, Maxwell School, Syracuse University.
    2. Lixiong Yang & Mingjian Ren & Jianming Bai, 2025. "Threshold mixed data sampling logit model with an application to forecasting US bank failures," Empirical Economics, Springer, vol. 68(1), pages 433-477, January.
    3. Seo, Myung Hwan & Koo, Bonsoo & Yang, Yangzhuoran Fin, 2024. "Nonlinear dynamics of Kimchi premium," Economic Modelling, Elsevier, vol. 135(C).

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics

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