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Axiomatizing Local Asymptotic Minimax Risk — arXiv:2609.19738

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19738
License (as archived): CC0-1.0
Archived: 2026-10-10T06:16:59.696Z
SHA-256 of the archived text: 3eee8469776e2e2a85569b9c453c93a5faafd4459f3072ca2d79d4b06f6d2c86
Stable URL of this page: https://metraipolis.com/documento/dc_7cdff79b6956

How to cite

Axiomatizing Local Asymptotic Minimax Risk — arXiv:2609.19738 — arXiv (en), https://arxiv.org/abs/2609.19738 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7cdff79b6956 (Metraipolis archive dc_7cdff79b6956, sha256 3eee8469776e2e2a85569b9c453c93a5faafd4459f3072ca2d79d4b06f6d2c86)

BibTeX

@misc{dc7cdff79b6956,
  title = {Axiomatizing Local Asymptotic Minimax Risk — arXiv:2609.19738},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19738},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7cdff79b6956; sha256 3eee8469776e2e2a85569b9c453c93a5faafd4459f3072ca2d79d4b06f6d2c86},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19738. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\alpha$-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 $\alpha$-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.

Tema degli esploratori: economia dei servizi IA (retro-catalogo arXiv: annunci del 2026-09-18 in econ.EM).
Categorie arXiv: Econometrics (econ.EM) ; Theoretical Economics (econ.TH).
Pagina del lavoro: https://arxiv.org/abs/2609.19738 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T05:56:02.771Z dalla pagina https://arxiv.org/catchup/econ.EM/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).