  Motivated by various computational applications, we investigate the problem
of estimating nested expectations. Building upon recent work by the authors, we
propose a novel Monte Carlo estimator for nested expectations, inspired by
sparse grid quadrature, that does not require sampling from inner conditional
distributions. Theoretical analysis establishes an upper bound on the mean
squared error of our estimator under mild assumptions on the problem,
demonstrating its efficiency for cases with low-dimensional outer variables. We
illustrate the effectiveness of our estimator through its application to
problems related to value of information analysis, with moderate
dimensionality. Overall, our method presents a promising approach to
efficiently estimate nested expectations in practical computational settings.
