Stone's theorem for distributional regression in Wasserstein distance

02/02/2023
by   Clément Dombry, et al.
0

We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide universally consistent estimates of the conditional distributions, where the error is measured by the Wasserstein distance of order p ≥ 1. Furthermore, for p = 1, we determine the minimax rates of convergence on specific classes of distributions. We finally provide some applications of these results, including the estimation of conditional tail expectation or probability weighted moment.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset