Abstract

When data are scare or samples very small, then exact inference is hardly possible. Moreover, if a given samples size is reasonably, that depends on the complexity of the estimation problem. We start from the simple problem of estimating a mean of a scalar variable or the correlation of two variables and providing a reliable confidence interval even if the sample is very small. Without distributional assumptions, bootstrap is so far the maybe most common approach. However, depending on the distribution of the original variable(s), its coverage properties can be very poor. We show how a relatively simple regularization by optimal transport can significantly improve on it. Our method is theoretically valid but fully data-driven in practice. This talk is based on joint work with Christophe Valvason and Eustasio del Barrio.