The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses

• URL: http://arxiv.org/abs/2607.28861v1
• Date: Thu, 30 Jul 2026 22:01:08 GMT
• Title: The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses
• Abstract summary: The parametric score test assesses a hypothesis through derivatives of the log-likelihood, whose expectation vanishes under the null.<n>This yields goodness-of-fit tests for common semiparametric regression models.<n>We show the test has power whenever the hunted direction is correlated with the true score.
• Score: 1.7969777786551424
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

Related papers

• Goodness-of-Fit Tests and Calibration Machine-Learning Algorithms for Logistic Regression with Sparse Data [0.0]
  This thesis studies classical GOF tests for binary logistic regression under both grouped and sparse data.<n>It shows that many of these tests fail to give valid conclusions when exposed to the complexities of actual datasets.
  arXiv  Detail & Related papers  (2026-08-11T17:00:50Z)
• When prompt perturbations break your A/B test: A valid statistical test for generative surveying [0.3366038232188622]
  We show that standard hypothesis tests, including the sign test and Wilcoxon signed-rank test, are invalid under a statistical model for generative surveying.<n>We propose a permutation test that is valid under this model and formally characterize the conditions under which standard tests fail.
  arXiv  Detail & Related papers  (2026-05-26T00:35:58Z)
• A Theoretical Framework for Statistical Evaluability of Generative Models [57.9316356505791]
  We introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics.<n>We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs) and Rényi divergences.<n>We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors.<n>In contrast, Rényi and KL divergences are not evaluable from finite samples, as their values can be critically determined by rare events.
  arXiv  Detail & Related papers  (2026-04-07T01:53:59Z)
• Pre-validation Revisited [79.92204034170092]
  We show properties and benefits of pre-validation in prediction, inference and error estimation by simulations and applications.<n>We propose not only an analytical distribution of the test statistic for the pre-validated predictor under certain models, but also a generic bootstrap procedure to conduct inference.
  arXiv  Detail & Related papers  (2025-05-21T00:20:14Z)
• Precise Error Rates for Computationally Efficient Testing [67.30044609837749]
  We revisit the question of simple-versus-simple hypothesis testing with an eye towards computational complexity.<n>An existing test based on linear spectral statistics achieves the best possible tradeoff curve between type I and type II error rates.
  arXiv  Detail & Related papers  (2023-11-01T04:41:16Z)
• Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling [82.36856860383291]
  We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method.
  arXiv  Detail & Related papers  (2023-10-27T13:09:56Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Learning to Increase the Power of Conditional Randomization Tests [8.883733362171032]
  The model-X conditional randomization test is a generic framework for conditional independence testing. We introduce novel model-fitting schemes that are designed to explicitly improve the power of model-X tests.
  arXiv  Detail & Related papers  (2022-07-03T12:29:25Z)
• Diagnostic Tool for Out-of-Sample Model Evaluation [12.44615656370048]
  We consider the use of a finite calibration data set to characterize the future, out-of-sample losses of a model. We propose a simple model diagnostic tool that provides finite-sample guarantees under weak assumptions.
  arXiv  Detail & Related papers  (2022-06-22T11:13:18Z)
• Significance tests of feature relevance for a blackbox learner [6.72450543613463]
  We derive two consistent tests for the feature relevance of a blackbox learner. The first evaluates a loss difference with perturbation on an inference sample. The second splits the inference sample into two but does not require data perturbation.
  arXiv  Detail & Related papers  (2021-03-02T00:59:19Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Achieving Equalized Odds by Resampling Sensitive Attributes [13.114114427206678]
  We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. We develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature.
  arXiv  Detail & Related papers  (2020-06-08T00:18:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.