Gary Cornwall, Jeff Chen, Beau Sauley
arXiv 2 Mar 2021 · Econometrics · 1 citations (OpenAlex)
arXiv:2103.01368 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Neyman, J. and E. S. Pearson (1933) The testing of statistical hypotheses in relation to probabilities a priori | 1.000 | 6 | 3 | 100% |
| 2 | Schapire, R. E. and Y. Freund (2013) Boosting: Foundations and algorithms | 0.874 | 6 | 2 | 100% |
| 3 | Kuhn, M., K. Johnson, et al (2013) Applied predictive modeling, Volume 26 | 0.843 | 3 | 3 | 100% |
| 4 | Chen, T. and C. Guestrin (2016) Xgboost: A scalable tree boosting system | 0.811 | 4 | 2 | 100% |
| 5 | Dickey, D. A. and W. A. Fuller (1981) Likelihood ratio statistics for autoregressive time series with a unit root | 0.811 | 4 | 2 | 100% |
| 6 | Kwiatkowski, D., P. C. Phillips, P. Schmidt, Y. Shin, et al (1992) Testing the null hypothesis of stationarity against the alternative of a unit root | 0.811 | 4 | 2 | 100% |
| 7 | Nelson, C. R. and C. R. Plosser (1982) Trends and random walks in macroeconmic time series: some evidence and implications | 0.811 | 4 | 2 | 100% |
| 8 | Breiman, L (2001) Random forests | 0.737 | 3 | 2 | 100% |
| 9 | Neyman, J. and E. S. Pearson (1933) Ix. on the problem of the most efficient tests of statistical hypotheses | 0.737 | 3 | 2 | 100% |
| 10 | Perron, P (1989) The great crash, the oil price shock, and the unit root hypothesis | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 107 scored citations.