  In stochastic simulation, input uncertainty refers to the output variability
arising from the statistical noise in specifying the input models. This
uncertainty can be measured by a variance contribution in the output, which, in
the nonparametric setting, is commonly estimated via the bootstrap. However,
due to the convolution of the simulation noise and the input noise, the
bootstrap consists of a two-layer sampling and typically requires substantial
simulation effort. This paper investigates a subsampling framework to reduce
the required effort, by leveraging the form of the variance and its estimation
error in terms of the data size and the sampling requirement in each layer. We
show how the total required effort can be reduced from an order bigger than the
data size in the conventional approach to an order independent of the data size
in subsampling. We explicitly identify the procedural specifications in our
framework that guarantee relative consistency in the estimation, and the
corresponding optimal simulation budget allocations. We substantiate our
theoretical results with numerical examples.
