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Minimax Risk in Estimating Kink Threshold and Testing Continuity

Javier Hidalgo (London School of Economics, London, UK)

Heejun Lee (Brown University, Providence, RI, USA)

Jungyoon Lee (Royal Holloway, University London, London, UK)

Myung Hwan Seo (Seoul National University, Seoul, Korea)

Essays in Honor of Joon Y. Park: Econometric Theory

ISBN: 978-1-83753-209-4, eISBN: 978-1-83753-208-7

Publication date: 24 April 2023

Abstract

The authors 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, the authors 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.

Keywords

Acknowledgements

Acknowledgments

Seo gratefully acknowledges the support from the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2020S1A5A2A03046422) and from the Research Grant of the Center for Distributive Justice at the Institute of Economic Research, Seoul National University. Hidalgo acknowledges financial support from STICERD under the grant “Testing Economic Shape Restrictions.”

Citation

Hidalgo, J., Lee, H., Lee, J. and Seo, M.H. (2023), "Minimax Risk in Estimating Kink Threshold and Testing Continuity", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Theory (Advances in Econometrics, Vol. 45A), Emerald Publishing Limited, Leeds, pp. 233-259. https://doi.org/10.1108/S0731-90532023000045A008

Publisher

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Emerald Publishing Limited