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

In this paper we have updated the hypothesis testing framework by drawing\nupon modern computational power and classification models from machine\nlearning. We show that a simple classification algorithm such as a boosted\ndecision stump can be used to fully recover the full size-power trade-off for\nany single test statistic. This recovery implies an equivalence, under certain\nconditions, between the basic building block of modern machine learning and\nhypothesis testing. Second, we show that more complex algorithms such as the\nrandom forest and gradient boosted machine can serve as mapping functions in\nplace of the traditional null distribution. This allows for multiple test\nstatistics and other information to be evaluated simultaneously and thus form a\npseudo-composite hypothesis test. Moreover, we show how practitioners can make\nexplicit the relative costs of Type I and Type II errors to contextualize the\ntest into a specific decision framework. To illustrate this approach we revisit\nthe case of testing for unit roots, a difficult problem in time series\neconometrics for which existing tests are known to exhibit low power. Using a\nsimulation framework common to the literature we show that this approach can\nimprove upon overall accuracy of the traditional unit root test(s) by seventeen\npercentage points, and the sensitivity by thirty six percentage points.\n

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