Model-Robust Interval Estimation

Confidence intervals are one of the most useful statistical tools. This dissertation is a study of several methods for forming confidence intervals that are insensitive to model assumptions, provided that the mean model for the data is not misspecified. The most commonly used robust confidence interval, the generalized Wald interval, is known to be liberal in small sample situations. We investigate several alternatives to the generalized Wald interval that are shown to often have superior performance: the generalized score interval; the robust profile likelihood interval; a new, modified generalized score interval that we call the GS2 interval; and we investigate a bootstrap calibration of the generalized Wald interval. We also introduce a new general procedure, length-optimal interval estimation, that takes an existing equal-tail confidence procedure and creates a new one whose length is shorter than the original. Surprisingly, in simulations we see that these shorter intervals are shown to sometimes enjoy higher coverage than their standard counterparts.