Hypothesis testing in adaptively sampled data: ART to maximize power beyond iid sampling
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Dae Woong Ham [1] ; Jiaze Qiu [1]
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[1] Harvard University
Harvard University
City of Cambridge, Estados Unidos
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 3, 2023, págs. 998-1037
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Testing whether a variable of interest affects the outcome is one of the most fundamental problems in statistics and is often the main scientific question of interest. To tackle this problem, the conditional randomization test (CRT) is widely used to test the independence of variable(s) of interest (X) with an outcome (Y) holding other variable(s) (Z) fixed. The CRT uses “Model-X” inference framework that relies solely on the iid sampling of (X, Z) to produce exact finite-sample p values that are constructed using any test statistic. We propose a new method, the adaptive randomization test (ART), that tackles the same independence problem while allowing the data to be adaptively sampled. Like the CRT, the ART relies solely on knowing the (adaptive) sampling distribution of (X, Z). Although the ART allows practitioners to flexibly design and analyze adaptive experiments, the method itself does not guarantee a powerful adaptive sampling procedure. For this reason, we show substantial power gains obtained from adaptively sampling compared to the typical iid sampling procedure in a multi-arm bandit setting and an application in conjoint analysis. We believe that the proposed adaptive procedure is successful because it takes arms that may initially look like “fake” signals due to random chance and stabilizes them closer to “null” signals and samples more/less from signal/null arms.
