In this paper, we propose a new algorithm to handle massive data sets, which are modelled by modal regression models. Differing from the existing methods regarding distributed modal regression, the proposed method combines the divide-and-conquer idea and a linear approximation algorithm. It is computationally fast and statistically efficient to implement. Theoretical analysis for the resultant distributed estimator under some regularity conditions is presented. Simulation studies are conducted to assess the effectiveness and flexibility of the proposed method with a finite sample size. Finally, an empirical application to the chemical sensors data is analysed for further illustration.

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To cite this article: Xuejun Ma & Xiaochao Xia (2025) An algorithm for distributed parameter estimation in modal regression models, Statistical Theory and Related Fields, 9:2, 101-123, DOI: 10.1080/24754269.2025.2483553

To link to this article: https://doi.org/10.1080/24754269.2025.2483553