Ricky Li
arXiv 17 Sep 2026 · Econometrics
arXiv:2609.19738 · PDF · Extracted main text
Local asymptotic minimax (LAM) risk is a foundational efficiency criterion in statistics and econometrics. The literature uses two definitions of LAM risk: one which appears in classical lower bounds and another which appears in arguments establishing attainment of those bounds. Conventional efficiency arguments are consistent with any estimator-dependent weighted average of the two, and consequently do not reveal which of these generalized $α$-LAM risk indices describes researchers' actual preferences. We take a decision-theoretic approach to systematically resolve this ambiguity. We axiomatically characterize the set of preferences with a generalized $α$-LAM representation, and we document that such preferences may violate basic rationality requirements such as Monotonicity. Motivated by this, we axiomatically characterize the subset with constant-weight representations. Within this class, a Sample Uncertainty Aversion axiom uniquely selects attainment LAM. We argue that Sample Uncertainty Aversion is normatively appealing, and we therefore recommend attainment LAM as the functional form for LAM risk.
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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 | |
|---|---|---|---|---|---|
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| 2 | Van der Vaart, Aad W (1998) Asymptotic Statistics | 0.916 | 13 | 3 | 77% |
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| 10 | Stoye, Jörg (2012) New perspectives on statistical decisions under ambiguity | 0.737 | 3 | 2 | 100% |
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