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Activity Number: 306 - SPEED: SPAAC SESSION II
Type: Topic-Contributed
Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
Sponsor: Biometrics Section
Abstract #318099
Title: A General Adaptive Framework for Testing a Multivariate Point Null Hypothesis
Author(s): Adam Elder* and Alex Luedtke and Marco Carone
Companies: University of Washington and University of Washington and University of Washington
Keywords: Hypothesis testing; nonparametric; multivariate point null; asymptotic linearity

In many disciplines, researchers are often interested in understanding the relationship between an outcome and a large set of covariates. A first step to investigating such relationships is to screen covariates for an association with the outcome. This screening can be achieved using a variety of approaches, from general methods to techniques tailored to a single problem. Existing methods that can be applied across a variety of problems frequently have lower power. Tailor-made procedures tend to attain higher power by building their procedures around problem-specific information but typically cannot be easily adapted to new settings. We propose a general framework for testing the existence of an association between an outcome and any number of covariates in which the test statistic is adaptively selected to maximize power. We present theoretical guarantees for our test under fixed and local alternatives. We then show numerically that tests created using our framework can perform about as well as tailor-made methods when the latter are available. Finally, we develop tests in two settings in which tailor-made methods are not currently available.

Authors who are presenting talks have a * after their name.

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