Confidence Interval Robustness with Long-Tailed Symmetric Distributions

Abstract A variety of 95-percent confidence interval procedures have been examined in some detail using Monte Carlo techniques. These estimators were tried on simulated samples of sizes 10 and 20 from a spectrum of distributions ranging from the Gaussian to the long-tailed Cauchy. The robustness of an estimator is measured by both the closeness of its level to the 5-percent goal (robustness of validity) and its expected length as compared to its competitors (robustness of efficiency). Results include some quite robust procedures including some of the point M-estimators from the Princeton Robustness Study.