Neyman smooth-type goodness-of-fit tests in complex surveys

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).