Work

Confidence intervals for Newton–Cotes quadratures based on stationary point processes

Year: 2025

Type: article

Abstract: 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.

Source: Statistical Methods & Applications

DOI: 10.1007/s10260-024-00773-x

Authors: Mads Stehr, Markus Kiderlen

Institutions: Copenhagen Business School, Aarhus University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Copenhagen Business School