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About this paper
Lucas Darius Konrad, Nikolas Kuschnig
Konrad and Kuschnig introduce a formal statistical framework to determine if the maximal influence exerted by data subsets on statistical models is excessive or consistent with natural sampling variation. The work establishes an exact influence formula for linear regression and leverages extreme value theory to derive asymptotic distributions for maximal influence, enabling rigorous hypothesis testing.
Key insights
- Traditional first-order influence functions systematically underestimate the impact of groups of data points and extreme cases, necessitating an exact formula for accurate assessment.
- The asymptotic distribution of maximal influence depends critically on the size of the influential set (constant vs. growing with sample size) and the tail characteristics of the data (heavy-tailed distributions lead to Fréchet, light-tailed or growing sets to Gumbel).
- Maximal influence, as an extremal quantity, is governed by Extreme Value Theory, providing a principled statistical foundation for its evaluation that moves beyond classical asymptotic approximations.
Summary by alphaXiv.
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