Prediction regions for bivariate extreme events

This paper suggests using a mixture of parametric and non-parametric methods to construct prediction regions in bivariate extreme-value problems. The non-parametric part of the technique is used to estimate the dependence function, or copula, and the parametric part is employed to estimate the marginal distributions. A bootstrap calibration argument is suggested for reducing coverage error. This combined approach is compared with a more parametric one, relative to which it has the advantages of being more flexible and simpler to implement. It also enjoys these features relative to predictive likelihood methods. The paper shows how to construct both compact and semi-infinite bivariate prediction regions, and it treats the problem of predicting the value of one component conditional on the other. The methods are illustrated by application to Australian annual maximum temperature data.