Robust Confidence Intervals for a Location Parameter: The Configural Approach

Abstract

Abstract A conditional approach to robustness is described and applied to interval estimation for a location parameter. Two new types of confidence interval estimators using two-dimensional numerical integrations within location-and-scale configurations emerge. Strong confidence intervals have robust conditional coverage probabilities. Bioptimal confidence intervals are as short as possible and have robust overall coverage probabilities. Robust intervals compromising the Gaussian and the slash distributions serve as examples. A comparison with a variety of other confidence intervals shows the nonrobustness of rank-based interval estimators. For samples of size 10, robust intervals based on M-estimators are clearly superior. Tuning constants must be chosen carefully for interval estimation. An interval based on Tukey's biweight, for example, should be used with tuning constants of about 7, 8, and 11 for samples of size 20, 10, and 5, respectively.