Efficient Test for Threshold Regression Models in Short Panel Data

  • DOUNIA BOURZIK LMA, FSTT, Abdelmalek Essaadi University, Tetouan, Morocco
  • AZIZ LMAKRI AIMCE laboratory, ENSAM, Hassan II University, Casablanca, Morocco
  • AMAL MELLOUK Regional Center for Education and Training Trades, Tangier, Morocco
  • ABDELHADI AKHARIF LMA, FSTT, Abdelmalek Essaadi University, Tetouan, Morocco
DOI: https://doi.org/10.19139/soic-2310-5070-3091
Keywords: Threshold Regression Model, Local Asymptotic Normality, Local Asymptotic Linearity, Panel Data, Gaussian Tests, Adaptive Tests

Abstract

In this paper, we propose locally and asymptotically optimal tests (as defined in the Le Cam sense) that are parametric, Gaussian, and adaptive. These tests aim to address the problem of testing the classical regression model against the threshold regression model in short panel data, where n is large and T is small. The foundation of these tests is the Local Asymptotic Normality (LAN) property. We derive the asymptotic relative efficiencies of these tests, specifically in comparison to the Gaussian parametric tests. The results demonstrate that the adaptive tests exhibit higher asymptotic power than the Gaussian tests. Additionally, we conduct simulation studies and analyze real data to evaluate the performance of the suggested tests, and the results confirm their excellent performance.
Published
2025-12-15
How to Cite
BOURZIK, D., LMAKRI, A., MELLOUK, A., & AKHARIF, A. (2025). Efficient Test for Threshold Regression Models in Short Panel Data. Statistics, Optimization & Information Computing, 15(3), 1611-1631. https://doi.org/10.19139/soic-2310-5070-3091
Issue
Vol 15 No 3 (2026)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).