Asymptotic Variance of Newton-Cotes Quadratures based on Randomized Sampling Points

Mads Stehr, Markus Kiderlen

Publikation: Working paperForskning

Abstrakt

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.
OriginalsprogEngelsk
UdgivelsesstedAarhus
UdgiverCentre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University
Antal sider33
StatusUdgivet - 2019
Udgivet eksterntJa
NavnCSGB Research Reports
Nummer2

Emneord

  • Point processes
  • Cavalieri estimator
  • Randomized Newton-Cotes quadrature
  • Numerical integration
  • Asymptotic variance bounds

Citationsformater