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A More Robust t-Test

Ulrich K. Mueller

arXiv 14 Jul 2020 · Econometrics · publishedThe Review of Economics and Statistics (2023) · 2 citations (OpenAlex)

arXiv:2007.07065 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the t-test. This is a particular problem under clustering, since the number of observations then corresponds to the number of clusters, and heterogeneity in cluster sizes induces a form of heavy tails. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the average of the remaining observations to construct a more robust alternative to the t-test. The new test is found to control size much more successfully in small samples compared to existing methods. Analytical results in the canonical inference for the mean problem demonstrate that the new test provides a refinement over the full sample t-test under more than two but less than three moments, while the bootstrapped t-test does not.

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36
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55
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Bentkus and Gtze (1996) The Berry-Esseen Bound for Student's Statistic0.87452100%
2Bloznelis and Putter (2003) Second-order and bootstrap approximation to Student's t-statistic0.84333100%
3Elliott, Müller, and Watson (2015) Nearly Optimal Tests When a Nuisance Parameter is Present Under the Null Hypothesis0.81142100%
4Reiss (1989) Approximate distributions of order statistics: with applications to nonparametric statistics0.73732100%
5Hall and Wang (2004) Exact Convergence Rate and Leading Term in Central Limit Theorem for Student's T Statistic0.64422100%
6Müller (2019) Refining the central limit theorem approximation via extreme value theory0.64422100%
7Müller and Wang (2017) Fixed-k Asymptotic Inference about Tail Properties0.64422100%
8Imbens and Kolesar (2016) Robust Standard Errors in Small Samples: Some Practical Advice0.58531100%
9Bahadur and Savage (1956) The Non-Existence of Certain Statistical Procedures in Nonparametric Problems0.51121100%
10Johansson (2003) Estimating the Mean of Heavy-Tailed Distributions0.51121100%

Showing the top 10 of 36 scored citations.