  A method for the multifidelity Monte Carlo (MFMC) estimation of statistical
quantities is proposed which is applicable to computational budgets of any
size. Based on a sequence of optimization problems each with a globally
minimizing closed-form solution, this method extends the usability of a well
known MFMC algorithm, recovering it when the computational budget is large
enough. Theoretical results verify that the proposed approach is at least as
optimal as its namesake and retains the benefits of multifidelity estimation
with minimal assumptions on the budget or amount of available data, providing a
notable reduction in variance over simple Monte Carlo estimation.
