The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses
Abstract
The parametric score test assesses a hypothesis through derivatives of the log-likelihood, whose expectation vanishes under the null. When the parameter of interest is a regression function identified as a risk minimiser, we extend this idea to test whether it belongs to a given linear function class. This yields goodness-of-fit tests for common semiparametric regression models, including generalised additive and partially linear models. Suitably formulated, the framework also detects effect modifiers in observational studies. We propose a hunt-and-test strategy that splits the data into two: on one part, after fitting the null model, machine learning is used to identify a promising direction in the empirical scores; on the other, we test whether the score vanishes in that direction. To account for error in estimating the null model, we apply a debiasing correction based on a weighted least squares projection. We establish Type I error control under relatively mild conditions and show the test has power whenever the hunted direction is correlated with the true score. Simulations and real-data examples demonstrate favourable performance, including identifying effect modifiers in an HIV clinical trial and assessing an additive model for insurance claims. The methodology is implemented in the R package dScoreTest.
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BibTeX
@misc{dhawan2026debiased,
title = {{The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses}},
author = {Aditya Dhawan and F. Richard Guo and Rajen D. Shah},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.28861},
eprint = {2607.28861},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28861},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses
AU - Aditya Dhawan
AU - F. Richard Guo
AU - Rajen D. Shah
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.28861
UR - https://arxiv.org/abs/2607.28861
AB - The parametric score test assesses a hypothesis through derivatives of the log-likelihood, whose expectation vanishes under the null. When the parameter of interest is a regression function identified as a risk minimiser, we extend this idea to test whether it belongs to a given linear function class. This yields goodness-of-fit tests for common semiparametric regression models, including generalised additive and partially linear models. Suitably formulated, the framework also detects effect modifiers in observational studies. We propose a hunt-and-test strategy that splits the data into two: on one part, after fitting the null model, machine learning is used to identify a promising direction in the empirical scores; on the other, we test whether the score vanishes in that direction. To account for error in estimating the null model, we apply a debiasing correction based on a weighted least squares projection. We establish Type I error control under relatively mild conditions and show the test has power whenever the hunted direction is correlated with the true score. Simulations and real-data examples demonstrate favourable performance, including identifying effect modifiers in an HIV clinical trial and assessing an additive model for insurance claims. The methodology is implemented in the R package dScoreTest.
ER -