Variance stabilizing transformations, studentization and the bootstrap

This paper compares higher order asymptotic properties of confidence intervals based on studentization and variance stabilizing transformations. Expansions for the coverage probabilities and lengths of (two-sided) confidence intervals with normal critical points are obtained. The comparison is carried out further for bootstrap confidence intervals based on the pivotal quantities derived from these methods. The results are illustrated with two examples involving (i) a location-scale model and (ii) one parameter exponential family of distributions. Furthermore, generalizations to the case where the asymptotic variance of the estimator sequence of interest depends on nuisance parameters are also given. It follows from these results that neither of the methods outperforms the other in all situations, and hence the expansions given here can be used effectively to determine the better method in a specific application.