Speeding Up the Asymptotics When Constructing One-sided Coverage Intervals with Survey Data
Kott, P. S. (2009, August). Speeding Up the Asymptotics When Constructing One-sided Coverage Intervals with Survey Data. Presented at Joint Statistical Meetings 2009, Washington, DC.
Coverage intervals for a parameter estimate are frequently derived from a survey sample by assuming that the randomization-based parameter estimate is asymptotically normal and that the associated measure of the estimator’s variance is roughly chi-squared. In many situations, however, the size of the sample and the nature of the parameter being estimated render the conventional Wald technique dubious, especially when a one-sided coverage interval is needed. We will propose a method of coverage-interval construction that “speeds up the asymptotics” so that the resulting one-sided intervals can have much better coverage properties than corresponding Wald intervals. For the important case of a mean computed from a stratified, simple random sample with ignorably small sampling fractions, no model need be assumed. Moreover, whether or not a model is invoked, our intervals are asymptotically equivalent to Wald intervals. As a result, they share the same large-sample, randomization-based properties. A simulation confirms the usefulness of our intervals.