Benedikt M. Pötscher, David Preinerstorfer
arXiv 26 Apr 2021 · Mathematics — Statistics Theory · publishedEconometric Theory (2023) · 4 citations (OpenAlex)
arXiv:2104.12597 · PDF · DOI · OpenAlex · Extracted main text
Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions; and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to over-rejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.
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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 | Bakirov, N. and Székely, G (2005) Student's t-test for Gaussian scale mixtures | 1.000 | 9 | 3 | 100% |
| 2 | Ibragimov, R. and Müller, U. K (2016) Inference with few heterogeneous clusters | 1.000 | 9 | 3 | 100% |
| 3 | Davidson, R. and MacKinnon, J. G (1985) Heteroskedasticity-robust tests in regressions directions | 0.874 | 8 | 2 | 100% |
| 4 | Bakirov, N. K (1998) Nonhomogeneous samples in the Behrens-Fisher problem | 0.874 | 6 | 2 | 100% |
| 5 | Pötscher, B. M. and Preinerstorfer, D (2022) How reliable are bootstrap-based heteroskedasticity robust tests? self | 0.794 | 10 | 7 | 50% |
| 6 | Pötscher, B. M. and Preinerstorfer, D (2019) Further results on size and power of heteroskedasticity and autocorrelation robust tests, with an application to trend testing self | 0.763 | 9 | 7 | 44% |
| 7 | Preinerstorfer, D (2021) hrt: Heteroskedasticity Robust Testing self | 0.759 | 16 | 6 | 44% |
| 8 | Duchesne, P. and de Micheaux, P. L (2010) Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods | 0.737 | 3 | 3 | 67% |
| 9 | Mickey, M. R. and Brown, M. B (1966) Bounds on the distribution functions of the Behrens-Fisher statistic | 0.737 | 3 | 3 | 67% |
| 10 | Bell, R. M. and McCaffrey, D (2002) Bias reduction in standard errors for linear regression with multi-stage samples | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 53 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Necessary and Sufficient Condition for Size Controllability of Heteroskedasticity Robust Test Statistics | 0.839 | 78 | 6 |
| 2 | How Reliable are Bootstrap-based Heteroskedasticity Robust Tests? | 0.794 | 8 | 4 |
| 3 | Inference with few treated units | 0.644 | 3 | 2 |
| 4 | Occasionally Misspecified | 0.405 | 1 | 1 |