On the bootstrap and likelihood-based confidence regions

Abstract

We describe a method for constructing likelihood-based confidence regions for a vector parameter, using the bootstrap and nonparametric density estimation. The technique is illustrated by application to a numerical example, and its theoretical properties are elucidated. It is argued that likelihood-based regions should not be approximated by ellipses, if we are to have any hope of capturing first-order departures from normality. Bootstrap algorithms for constructing simultaneous confidence intervals for the components of a vector parameter are also presented. Advantages of the percentile- t method over the ordinary percentile method are demonstrated in a multivariate setting.