Simplex-based multinomial logistic regression with diverging numbers of categories and covariate
Sheng Fu (National University of Singapore)
P. Chen (TU Delft - Statistics)
Yufeng Liu (University of North Carolina)
Zhi Sheng Ye (National University of Singapore)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.