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Minimax Risk in Estimating Kink Threshold and Testing Continuity

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  • Javier Hidalgo
  • Heejun Lee
  • Jungyoon Lee
  • Myung Hwan Seo

Abstract

We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size $ n $ grows only at the cube root rate. Motivated by this finding, we develop a continuity test for the threshold regression model and a bootstrap to compute its \textit{p}-values. The validity of the bootstrap is established, and its finite sample property is explored through Monte Carlo simulations.

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  • Javier Hidalgo & Heejun Lee & Jungyoon Lee & Myung Hwan Seo, 2022. "Minimax Risk in Estimating Kink Threshold and Testing Continuity," Papers 2203.00349, arXiv.org.
    • Handle: RePEc:arx:papers:2203.00349
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    References listed on IDEAS

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    1. Chang, Yoosoon & Choi, Yongok & Park, Joon Y., 2017. "A new approach to model regime switching," Journal of Econometrics, Elsevier, vol. 196(1), pages 127-143.
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