Verify DRIS performance under non-Gaussian elliptical nominal distributions

Establish the theoretical performance of the Distributionally Robust Importance Sampling (DRIS) estimator, defined for computing worst-case rare-event probabilities over a 2-Wasserstein ball centered at a nominal distribution, when the nominal distribution belongs to a multivariate elliptical family beyond the Gaussian case. Specifically, determine whether DRIS retains its proven properties (such as asymptotic behavior and efficiency) under non-Gaussian elliptical nominal distributions and characterize any conditions required for these guarantees.

Background

The paper introduces Distributionally Robust Importance Sampling (DRIS) to estimate worst-case rare-event probabilities under distributional model uncertainty, using a Wasserstein ambiguity set centered at a nominal distribution. The main theoretical guarantees are established under a Gaussian nominal distribution, including a central limit theorem and vanishing relative error.

In the concluding remarks, the authors note that while the DRIS framework naturally extends to other multivariate elliptical nominal distributions, the theoretical performance in these non-Gaussian cases has not been verified. Confirming DRIS’s performance beyond the Gaussian setting would broaden its applicability and solidify its theoretical foundations.