Robust confidence limits

Abstract

A location parameter is to be estimated from a sample of fixed size n, assuming that the shape of the true underlying distribution lies anywhere within ε of some given shape, e.g. the normal one. The metric in the space of distribution functions may be defined in various ways: total variation, Kolmogorov or Lévy distance. A minimax solution to this problem is described explicitly; it minimizes the maximum probability that the estimate exceeds, or falls below, the true value of the parameter by more than some fixed amount. © 1968 Springer-Verlag.