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