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

arXiv: https://arxiv.org/abs/2607.28861 · HTML: https://mlsanity.com/paper/2607.28861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [The Projected Covariance Measure for assumption-lean variable significance testing](https://mlsanity.com/paper/2211.02039/) (2022)
- [Goodness-of-fit testing in high-dimensional generalized linear models](https://mlsanity.com/paper/1908.03606/) (2019)
- [qgam: Bayesian non-parametric quantile regression modelling in R](https://mlsanity.com/paper/2007.03303/) (2020)
- [Goodness of fit tests for high-dimensional linear models](https://mlsanity.com/paper/1511.03334/) (2015)
- [Rank-transformed subsampling: inference for multiple data splitting and exchangeable p-values](https://mlsanity.com/paper/2301.02739/) (2023)
- [Variable importance measures for heterogeneous treatment effects with survival outcome](https://mlsanity.com/paper/2412.11790/) (2024)

## Built on by (most cited first, 1 of 1)

- [Toward a Semiparametric Efficiency Theory under Equality Constraints in Nested Markov Models](https://mlsanity.com/paper/2608.24602/) (2026)

## Abstract (arXiv)

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.