@techreport{44d426c10cf44ea596ee992f532e27eb,

title = "Asymptotic Variance of Newton-Cotes Quadratures based on Randomized Sampling Points",

abstract = "In this paper we consider the problem of numerical integration when sampling nodes are random, and we suggest to use Newton-Cotes quadrature rules to exploit smoothness properties of the integrand. In previous papers it was shown that a Riemann sum approach can cause a severe variance inflation when the sampling points are not equidistant. However, under some integrability conditions on the typical point-distance, we show that Newton-Cotes quadratures based on a stationary point process in R yield unbiased estimators for the integral and that the aforementioned variance inflation can be avoided if a Newton-Cotes quadrature of sufficiently high order is applied. In a stereological application, this corresponds to the estimation of volume of a compact object from area measurements on parallel sections. ",

keywords = "Point processes, Cavalieri estimator, Randomized Newton-Cotes quadrature, Numerical integration, Asymptotic variance bounds, Point processes, Cavalieri estimator, Randomized Newton-Cotes quadrature, Numerical integration, Asymptotic variance bounds",

author = "Mads Stehr and Markus Kiderlen",

year = "2019",

language = "English",

series = "CSGB Research Reports",

publisher = "Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University",

number = "2",

address = "Denmark",

type = "WorkingPaper",

institution = "Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University",

}