A0233
Title: Improved confidence intervals with optimal transportation theory
Authors: Christophe Valvason - University of Geneva (Switzerland) [presenting]
Stefan Sperlich - University of Geneva (Switzerland)
Abstract: Reliable inferential tools for small samples and complex statistics are of high importance in empirical research and official statistics. In this context, we aim to improve the estimation of confidence intervals by using methods developed along the optimal transport theory. When two probability measures satisfy some regularity constraints, the solution to Monge's problem is determined by the composition of the cdf and the quantile function. Clearly, in small samples, the empirical cdf is a step function with a few but large jumps, so the standard transportation map is not necessarily optimal. We propose to compute the optimal transportation plan between a probability distribution of reference that satisfies the regularity constraints and a bootstrap estimate of the probability measure of interest. Then, we construct an exact confidence interval inside the reference distribution and transport this to the problem of interest. Optimal transportation theory provides us with the tools to show the validity of our method. Simulations show that the proposed method gives confidence intervals with coverage closer to the nominal level and at the same time a smaller variance than both, direct and bootstrap confidence interval estimates.
