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An Asymptotic Framework for Closed-Form Estimators from Surrogate Estimating Equations — arXiv:2611.08746

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.08746
License (as archived): CC0-1.0
Archived: 2026-11-09T22:42:41.197Z
SHA-256 of the archived text: e00a382c7e40130cde3098caa3f818df14be20f8194f3ae98b8da5582f1ed0fc
Stable URL of this page: https://metraipolis.com/documento/dc_bc7ea9bcedac

How to cite

An Asymptotic Framework for Closed-Form Estimators from Surrogate Estimating Equations — arXiv:2611.08746 — arXiv (en), https://arxiv.org/abs/2611.08746 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bc7ea9bcedac (Metraipolis archive dc_bc7ea9bcedac, sha256 e00a382c7e40130cde3098caa3f818df14be20f8194f3ae98b8da5582f1ed0fc)

BibTeX

@misc{dcbc7ea9bcedac,
  title = {An Asymptotic Framework for Closed-Form Estimators from Surrogate Estimating Equations — arXiv:2611.08746},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.08746},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bc7ea9bcedac; sha256 e00a382c7e40130cde3098caa3f818df14be20f8194f3ae98b8da5582f1ed0fc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.08746. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many statistical estimators, including maximum likelihood and method of moments estimators, are defined as roots of estimating equations. In complex models, these equations often cannot be solved explicitly; although numerical methods can provide approximate solutions, closed-form approximations can reduce computation and facilitate theoretical analysis by making an estimator's dependence on the data more transparent. In this paper, we develop a general approach to constructing such approximations and a framework for quantifying their accuracy. Our theory accommodates sequences of parameters that approach the boundary of the parameter space or diverge to infinity, and provides conditions under which a closed-form approximate estimator has the same first-order asymptotic distribution as its exact counterpart. We focus on approximations to maximum likelihood estimators, although the theory applies to general estimating equations. We apply the framework to iid models from the gamma, zeta, von Mises, and generalized Pareto families, as well as to gamma regression. Together, these examples cover scalar and vector parameters, iid and non-iid settings, and normal and nonnormal asymptotic regimes. Each example is accompanied by a simulation study, and the gamma regression example also includes a real-world data application.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.08746 — 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 2026-11-09T22:35:47.232Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).