Asymptotic Analysis of Multilevel Best Linear Unbiased Estimators

We study the computational complexity and variance of multilevel best linear unbiased estimators introduced in [D. Schaden E. Ullmann, SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 601--635]. specialize results this work to PDE-based models that are parameterized by a discretization quantity, e.g., finite element mesh size. In particular, we investigate asymptotic so-called sample allocation optimal (SAOBs). These have smallest given fixed budget. However, SAOBs defined implicitly solving an optimization problem difficult analyze. Alternatively, class auxiliary based on Richardson extrapolation parametric model family. This allows us provide upper bound for SAOBs, showing their is within certain estimators. Moreover, not larger than Monte Carlo. The theoretical illustrated numerical experiments with elliptic PDE.