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arXiv · 2203.00349

Minimax Risk in Estimating Kink Threshold and Testing Continuity

Javier Hidalgo·Heejun Lee·Jungyoon Lee·Myung Hwan Seo
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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. 2022-03-01. Minimax Risk in Estimating Kink Threshold and Testing Continuity. https://arxiv.org/abs/2203.00349

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