Interval estimation of the population mean under model uncertainty: Robust versus empirical statistics

With reference to the problem of interval estimation of a population mean under model uncertainty, we compare approaches based on robust and empirical statistics via expected lengths of the associated confidence intervals. An explicit expression for confidence intervals arising from a general class of robust statistics is worked out and this is employed to obtain a higher order asymptotic formula for the expected lengths of such intervals. Comparative theoretical results, as well as a simulation study, are then presented.