Online Causal Inference Seminar: Hunt and test for assessing the fit of semiparametric regression models

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• Rajen Shah (University of Cambridge)
• Tuesday 02 December 2025, 16:30-17:30
• Discussion Room, Newton Institute.

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We consider testing the goodness of fit of semiparametric regression models, such as generalised additive models, partially linear models, and quantile additive regression models: a class of problems that includes, for example, testing for heterogeneous treatment effects. We propose an approach that involves splitting the data in two parts. On one part, we “hunt” for any signal that may be present in the score-type residuals following a fit of the null model. On the remaining data, we test for the presence of the potential signal thus found.  In the first, hunting stage of the procedure, our framework allows the use of any flexible regression method chosen by the practitioner, such as a random forest. The method can therefore harness the power of modern machine learning tools to detect complex alternatives. A challenge in the testing step is that any first-order bias in the residuals may lead to rejection under the null. To address this, we employ a debiasing step, which we show is equivalent to performing a particular weighted least squares regression. We establish that the type I error can be controlled under relatively mild conditions and that the test has power against alternatives for which, with high probability, the hunted signal is correlated with the true signal in the score residuals.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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