Consistency of randomized integration methods

Abstract

We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^p$ with $p>1$ consistency in terms of almost sure convergence

arXiv comment17 pages. Accepted for publication in Journal of Complexity

References in corpus (4)

• The role of Frolov's cubature formula for functions with bounded mixed derivative
• A Monte Carlo method for integration of multivariate smooth functions
• Construction-free median quasi-Monte Carlo rules for function spaces with unspecified smoothness and general weights
• Discrepancy Bounds for a Class of Negatively Dependent Random Points Including Latin Hypercube Samples

Cited by in corpus (1)

• A universal median quasi-Monte Carlo integration