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Nonparametric Regression with Multiple Thresholds: Estimation and Inference

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  • Yan-Yu Chiou
  • Mei-Yuan Chen
  • Jau-er Chen

Abstract

This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties of the local constant estimator for a nonparametric regression with multiple thresholds. However, the number of thresholds and corresponding threshold values are typically unknown in practice. We then use our testing procedure to determine the unknown number of thresholds and derive the limiting distribution of the proposed test. The Monte Carlo simulation results indicate the adequacy of the modified test and accuracy of the sequential estimation of the threshold values. We apply our testing procedure to an empirical study of the 401(k) retirement savings plan with income thresholds.

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  • Yan-Yu Chiou & Mei-Yuan Chen & Jau-er Chen, 2017. "Nonparametric Regression with Multiple Thresholds: Estimation and Inference," Papers 1705.09418, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1705.09418
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    References listed on IDEAS

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    Cited by:

    1. Takayuki Toda & Ayako Wakano & Takahiro Hoshino, 2019. "Regression Discontinuity Design with Multiple Groups for Heterogeneous Causal Effect Estimation," Papers 1905.04443, arXiv.org.
    2. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    3. Jau-er Chen & Chen-Wei Hsiang, 2019. "Causal Random Forests Model Using Instrumental Variable Quantile Regression," Econometrics, MDPI, vol. 7(4), pages 1-22, December.
    4. Christis Katsouris, 2023. "Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors," Papers 2305.00860, arXiv.org, revised May 2023.
    5. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    6. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    7. Dingwen Zhang, 2024. "Determining the Number and Values of Thresholds for Multi-regime Threshold Ornstein–Uhlenbeck Processes," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3581-3626, November.
    8. Jau-er Chen & Chien-Hsun Huang & Jia-Jyun Tien, 2021. "Debiased/Double Machine Learning for Instrumental Variable Quantile Regressions," Econometrics, MDPI, vol. 9(2), pages 1-18, April.
    9. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

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