Representative points for distribution recovering

This paper studies a scheme of producing representative points to approximate an arbitrary distribution or the unknown distribution of a given data. It leverages on the rich literature of space-filling designs on the unit hypercube, picks a good design and transforms it toward the distribution. This new approach is flexible and accurate in estimating the expected value of an expensive blackbox function over the underlying distribution. It accommodates any dependence structure among variables, and allows for any shape of supporting regions, including non-convex ones. Nested and sliced structures of the space-filling designs on the unit hypercube can be seamlessly preserved in the transformed space. Asymptotic properties of the resulting estimators are also established.