Print Email Facebook Twitter Simplex-based multinomial logistic regression with diverging numbers of categories and covariate Title Simplex-based multinomial logistic regression with diverging numbers of categories and covariate Author Fu, Sheng (National University of Singapore) Chen, P. (TU Delft Statistics) Liu, Yufeng (University of North Carolina) Ye, Zhisheng (National University of Singapore) Date 2023 Abstract Multinomial logistic regression models are popular in multicategory classification analysis, but existing models suffer several intrinsic drawbacks. In particular, the parameters cannot be determined uniquely because of the over-specification. Although additional constraints have been imposed to refine the model, such modifications can be inefficient and complicated. In this paper, we propose a novel and efficient simplex-based multinomial logistic regression technique, seamlessly connecting binomial and multinomial cases under a unified framework. Compared with existing models, our model has fewer parameters, is free of any constraints, and can be solved efficiently using the Fisher scoring algorithm. In addition, the proposed model enjoys several theoretical advantages, including Fisher consistency and sharp comparison inequality. Under mild conditions, we establish the asymptotical normality and convergence for the new model, even when the numbers of categories and covariates increase with the sample size. The proposed framework is illustrated by means of extensive simulations and real applications. Subject AsymptoticsclassificationFisher consistencykernel learningMLRsimplex coding scheme To reference this document use: http://resolver.tudelft.nl/uuid:7a749410-3d5d-4619-9f4b-94d57616fe6d DOI https://doi.org/10.5705/ss.202021.0082 Embargo date 2024-03-01 ISSN 1017-0405 Source Statistica Sinica, 33 (4), 2463-2493 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2023 Sheng Fu, P. Chen, Yufeng Liu, Zhisheng Ye Files PDF SMLR.pdf 1.31 MB Close viewer /islandora/object/uuid:7a749410-3d5d-4619-9f4b-94d57616fe6d/datastream/OBJ/view