Xu, JiazhenScealy, Janice L.Wood, Andrew T.A.Zou, Tao2025-12-232025-12-230047-259XORCID:/0000-0001-7415-908X/work/192496655ORCID:/0000-0002-9718-869X/work/192498786https://hdl.handle.net/1885/733796893Score matching is an estimation procedure that has been developed for statistical models whose probability density function or probability mass function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modeling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matching-based inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.This work was partially supported by ANU PhD scholarship from the Australian National University, Australia . The work of Janice L. Scealy and Andrew T. A. Wood was supported by Australian Research Council, Australia grant DP220102232 . The work of Tao Zou was supported by the assistance of computational resources provided by the Australian Government through the National Computational Infrastructure (NCI) under the ANU Startup Allocation Scheme.20enPublisher Copyright: © 2025 The Author(s)Auto modelCompositional data analysisConway–Maxwell–Poisson regressionFisher divergenceIntractable normalizing constant202510.1016/j.jmva.2025.105473105010203019