Autori: Stehr, Mads, Kiderlen, Markus
Titolo: Confidence intervals for Newton–Cotes quadratures based on stationary point processes
Periodico: Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2025 - Volume: 34 - Fascicolo: 1 - Pagina iniziale: 39 - Pagina finale: 67

Motivated by the stereological application of volume estimation, this paper is concerned with numerical integration on the real line, employing function values at a finite set of randomly chosen points. The sampling points are modeled by a stationary point process, with the estimators being Newton–Cotes quadratures. Our comprehensive probabilistic analysis crucially extends existing results regarding the approximation error and variance, accommodating more general integrands and non-ergodic sampling processes. Notably, these findings are used to formulate novel asymptotic confidence intervals, a considerable challenge given the usual absence of limit distributions. To underscore the practicality of our approach, we apply it to a stereological simulation study. Specifically, we establish confidence intervals for the volume of a three-dimensional ellipsoid, based on section areas obtained from randomly positioned parallel planes.




SICI: 1618-2510(2025)34:1<39:CIFNQB>2.0.ZU;2-M
Testo completo: https://link.springer.com/article/10.1007/s10260-024-00773-x

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