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In this paper we have updated the hypothesis testing framework by drawingupon modern computational power and classification models from machinelearning. We show that a simple classification algorithm such as a boosteddecision stump can be used to fully recover the full size-power trade-off forany single test statistic. This recovery implies an equivalence, under certainconditions, between the basic building block of modern machine learning andhypothesis testing. Second, we show that more complex algorithms such as therandom forest and gradient boosted machine can serve as mapping functions inplace of the traditional null distribution. This allows for multiple teststatistics and other information to be evaluated simultaneously and thus form apseudo-composite hypothesis test. Moreover, we show how practitioners can makeexplicit the relative costs of Type I and Type II errors to contextualize thetest into a specific decision framework. To illustrate this approach we revisitthe case of testing for unit roots, a difficult problem in time serieseconometrics for which existing tests are known to exhibit low power. Using asimulation framework common to the literature we show that this approach canimprove upon overall accuracy of the traditional unit root test(s) by seventeenpercentage points, and the sensitivity by thirty six percentage points.

Standing on the Shoulders of Machine Learning: Can We Improve Hypothesis Testing?