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Regression towards the mode

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  • Kemp, GCR
  • Santos Silva, JMC

Abstract

We propose a semi-parametric mode regression estimator for the case in which the variate of interest is continuous and observable over its entire un- bounded support. The estimator is semi-parametric in that the conditional mode is specified as a parametric function, but only mild assumptions are made about the nature of the conditional density of interest. We show that the proposed estimator is consistent and has a tractable asymptotic distribution. Simulation results and an empirical illustration are provided to highlight the practicality and usefulness of the estimator.

Suggested Citation

  • Kemp, GCR & Santos Silva, JMC, 2010. "Regression towards the mode," Economics Discussion Papers 5757, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:5757
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Weixin Yao & Longhai Li, 2014. "Acknowledgement of Priority," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1195-1195, December.
    2. Zhe Sun & Yundong Tu, 2024. "Factors in Fashion: Factor Analysis towards the Mode," Papers 2409.19287, arXiv.org.
    3. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jul 2024.
    4. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    5. Gordon C. R. Kemp & Paulo M. D. C. Parente & J. M. C. Santos Silva, 2020. "Dynamic Vector Mode Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 647-661, July.
    6. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    7. Baldauf, Markus & Santos Silva, J.M.C., 2012. "On the use of robust regression in econometrics," Economics Letters, Elsevier, vol. 114(1), pages 124-127.
    8. Jales, Hugo & Jiang, Boqian & Rosenthal, Stuart S., 2023. "JUE Insight: Using the mode to test for selection in city size wage premia," Journal of Urban Economics, Elsevier, vol. 133(C).
    9. Gianni Cicia & Marilena Furno & Teresa Giudice, 2021. "Do consumers’ values and attitudes affect food retailer choice? Evidence from a national survey on farmers’ market in Germany," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 9(1), pages 1-21, December.
    10. repec:esx:essedp:761 is not listed on IDEAS
    11. Shi, Jianhong & Zhang, Yujing & Yu, Ping & Song, Weixing, 2021. "SIMEX estimation in parametric modal regression with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    12. Lianqiang Yang & Wanli Yuan & Shijie Wang, 2025. "Modal regression models based on B-splines," Computational Statistics, Springer, vol. 40(1), pages 225-248, January.
    13. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2022. "Characterizing M-estimators," Papers 2208.08108, arXiv.org.
    14. Lv, Zhike & Zhu, Huiming & Yu, Keming, 2014. "Robust variable selection for nonlinear models with diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 90-97.
    15. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    16. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    17. Cheng Li & Ruihan Luo & Jian-Feng Yang, 2025. "Optimal distributed Poisson subsampling for modal regression with massive data," Statistical Papers, Springer, vol. 66(5), pages 1-32, August.
    18. Hongpeng Yuan & Sijia Xiang & Weixin Yao, 2024. "A new bandwidth selection method for nonparametric modal regression based on generalized hyperbolic distributions," Computational Statistics, Springer, vol. 39(4), pages 1729-1746, June.
    19. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    20. Hyun Kim & Yong-seong Kim & Myoung-jae Lee, 2012. "Treatment effect analysis of early reemployment bonus program: panel MLE and mode-based semiparametric estimator for interval truncation," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(3), pages 189-209, December.
    21. Yue Chao & Lei Huang & Xuejun Ma & Jiajun Sun, 2024. "Optimal subsampling for modal regression in massive data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(4), pages 379-409, May.
    22. Wang, Tao, 2025. "Semi-functional varying coefficient mode-based regression," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    23. Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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