Threshold regression with a threshold boundary

Ping Yu, Xiaodong Fan

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


This article studies computation, estimation, inference, and testing for linearity in threshold regression with a threshold boundary. We first put forward a new algorithm to ease the computation of the threshold boundary, and develop the asymptotics for the least squares estimator in both the fixed-threshold-effect framework and the small-threshold-effect framework. We also show that the inverting-likelihood-ratio method is not suitable to construct confidence sets for the threshold parameters, while the nonparametric posterior interval is still applicable. We then propose a new score-type test to test for the existence of threshold effects. Comparing with the usual Wald-type test, it is computationally less intensive, and its critical values are easier to obtain by the simulation method. Simulation studies corroborate the theoretical results. We finally conduct two empirical applications in labor economics to illustrate the nonconstancy of thresholds.

Original languageEnglish
Pages (from-to)953-971
Number of pages19
JournalJournal of Business and Economic Statistics
Issue number4
Publication statusPublished - 2021


  • Compound Poisson field
  • Epi-convergence
  • Poisson point process
  • Score test
  • Threshold boundary
  • Two-sided Brownian field

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