Bootstrap confidence intervals

The classical CIs for GEV or GP parameter estimates, calculated from the covariance matrices, are not exact because the sample size of the extremes, m, is not infinite. In addition to that, violations of the underlying model assumptions (Section 6.2.2.3) may increase the inexactness. In general, such situations favour the bootstrap approach to deliver more accurate results. However, in the case of CI construction for GEV or GP parameters and related quantities such as quantiles and return periods, bootstrap resampling may not always be preferable.

The problem with the nonparametric bootstrap resampling (Section 3.3.1) is that the distribution of the bootstrap replications does not uniformly converge with m to the true distribution when the parameter of interest is a quantile, see Bickel and Freedman (1981), Davison and Smith (1990: p. 440 therein) and Angus (1993). The alternative resampling, parametric surrogate data simulation (Section 3.3.3), has been found in Monte Carlo experiments (Caers et al. 1999a; Kysely 2008) to give CIs with acceptable accuracies—better than from nonparametric bootstrap resampling. The caveat against the method of parametric simulation, however, is that it prescribes a certain distribution model (GEV, GP) to draw data from and assumes its suitability. In practice, where m < to and the limiting model distribution has been only approximately approached, there comes additional uncertainty, which should widen the CIs obtained from parametric simulation. It is difficult to quantify how much wider accurate CIs would be.

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