去偏得分检验：半参数假设的搜寻-检验方法
The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses
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中文总结 AI 辅助
该研究提出去偏得分检验的搜寻-检验策略，用于半参数假设检验，可检验回归函数是否属于线性函数类，能识别效应修饰因子，在模拟和真实数据中表现良好，已实现为R包。
中文摘要 AI 辅助
参数得分检验通过对数似然的导数评估假设，在原假设下其期望为零。当关注参数为被识别为风险最小化器的回归函数时，我们将该思路扩展至检验其是否属于给定的线性函数类，由此得到常见半参数回归模型的拟合优度检验，包括广义加性模型和部分线性模型。经适当构建后，该框架还可识别观察性研究中的效应修饰因子。我们提出一种搜寻-检验策略，将数据分为两部分：在其中一部分上拟合原模型后，使用机器学习从经验得分中识别有前景的方向；在另一部分上检验该方向的得分是否为零。为考虑原模型估计的误差，我们应用基于加权最小二乘投影的去偏校正。我们在相对温和的条件下建立了一类错误控制，并证明当搜寻到的方向与真实得分相关时，该检验具有功效。模拟和真实数据示例验证了良好的性能，包括在一项HIV临床试验中识别效应修饰因子，以及评估保险索赔的加性模型。该方法已在R包dScoreTest中实现。
英文摘要
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.
