Hall, Peter On the bootstrap and likelihood-based confidence regions. (English) Zbl 0635.62033 Biometrika 74, 481-493 (1987). 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. Cited in 11 Documents MSC: 62G15 Nonparametric tolerance and confidence regions 62G05 Nonparametric estimation 62H12 Estimation in multivariate analysis Keywords:constructing likelihood-based confidence regions; vector parameter; density estimation; numerical example; first-order departures from normality; Bootstrap algorithms; simultaneous confidence intervals; percentile-t method; ordinary percentile method PDFBibTeX XMLCite \textit{P. Hall}, Biometrika 74, 481--493 (1987; Zbl 0635.62033) Full Text: DOI