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[2512.20007] Semiparametric KSD test: unifying score and distance-based approaches for goodness-of-fit testing
Summary
The paper introduces the Semiparametric Kernelized Stein Discrepancy (SKSD) test, a novel goodness-of-fit test that unifies score-based and distance-based approaches, demonstrating efficiency and consistency in model adequacy assessments.
Why It Matters
Goodness-of-fit tests are critical for validating statistical models. The SKSD test offers a new, efficient method that can handle complex models with intractable likelihoods, making it relevant for researchers and practitioners in machine learning and statistics.
Key Takeaways
- The SKSD test combines score-based and distance-based approaches for improved goodness-of-fit testing.
- It is computationally efficient and can accommodate general nuisance-parameter estimators.
- The test is universally consistent and achieves Pitman efficiency.
- It provides effective GoF tests for models with intractable likelihoods.
- The SKSD test demonstrates comparable power to traditional normality tests.
Statistics > Machine Learning arXiv:2512.20007 (stat) [Submitted on 23 Dec 2025 (v1), last revised 20 Feb 2026 (this version, v2)] Title:Semiparametric KSD test: unifying score and distance-based approaches for goodness-of-fit testing Authors:Zhihan Huang, Ziang Niu View a PDF of the paper titled Semiparametric KSD test: unifying score and distance-based approaches for goodness-of-fit testing, by Zhihan Huang and 1 other authors View PDF HTML (experimental) Abstract:Goodness-of-fit (GoF) tests are fundamental for assessing model adequacy. Score-based tests are appealing because they require fitting the model only once under the null. However, extending them to powerful nonparametric alternatives is difficult due to the lack of suitable score functions. Through a class of exponentially tilted models, we show that the resulting score-based GoF tests are equivalent to the tests based on integral probability metrics (IPMs) indexed by a function class. When the class is rich, the test is universally consistent. This simple yet insightful perspective enables reinterpretation of classical distance-based testing procedures-including those based on Kolmogorov-Smirnov distance, Wasserstein-1 distance, and maximum mean discrepancy-as arising from score-based constructions. Building on this insight, we propose a new nonparametric score-based GoF test through a special class of IPM induced by kernelized Stein's function class, called semiparametric kernelized Stein discrepancy (SKSD) t...
