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Minimax Risk in Estimating Kink Threshold and Testing Continuity

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

arXiv 1 Mar 2022 · Econometrics · 4 citations (OpenAlex)

arXiv:2203.00349 · PDF · DOI · OpenAlex · Extracted main text

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 p-values. The validity of the bootstrap is established, and its finite sample property is explored through Monte Carlo simulations.

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