In this study, we extend Neyman smooth-type goodness-of-fit tests to complex survey settings involving categorical data, by incorporating design-consistent estimators under the survey framework. This extension is implemented through data-driven, nonparametric order selection methods. We examine the asymptotic properties of the proposed estimators and demonstrate, through simulations, that our methods improve statistical power while maintaining strong control over Type I error, particularly in detecting subtle yet systematic differences across categories. We also illustrate the practical utility of our approach using data from the National Youth Tobacco Survey (NYTS).

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To cite this article: Yan Lu, Lang Zhou, Guoyi Zhang & Ronald Christensen (21 Jan 2026): Neyman smooth-type goodness-of-fit tests in complex surveys, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2026.2616882
To link to this article: https://doi.org/10.1080/24754269.2026.2616882