Semiparametric KSD Test: Unifying Score and Distance-Based Approaches for Goodness-of-Fit Testing
Analysis
This arXiv paper introduces a novel semiparametric kernelized Stein discrepancy (SKSD) test for goodness-of-fit. The core innovation lies in bridging the gap between score-based and distance-based GoF tests, reinterpreting classical distance-based methods as score-based constructions. The SKSD test offers computational efficiency and accommodates general nuisance-parameter estimators, addressing limitations of existing nonparametric score-based tests. The paper claims universal consistency and Pitman efficiency for the SKSD test, supported by a parametric bootstrap procedure. This research is significant because it provides a more versatile and efficient approach to assessing model adequacy, particularly for models with intractable likelihoods but tractable scores.
Key Takeaways
“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) test.”