GENERALIZED LEAST-SQUARES AND EMPIRICAL BAYES ESTIMATION IN REGIONAL PARTIAL DURATION SERIES INDEX-FLOOD MODELING

A regional estimation procedure that combines the index-flood concept with an empirical Bayes method for inferring regional information is i ntroduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior inform ation of the model parameters is inferred from regional data using gen eralized least squares (GLS) regression. Two different Bayesian T-year event estimators are introduced: a linear estimator that requires onl y some moments of the prior distributions to be specified and a parame tric estimator that is based on specified families of prior distributi ons. The regional method is applied to flood records from 48 New Zeala nd catchments. In the case of a strongly heterogeneous intersite corre lation structure, the GLS procedure provides a more efficient estimate of the regional GP shape parameter as compared to the usually applied weighted regional average. If intersite dependence is ignored, the un certainty of the regional estimator may be seriously underestimated an d erroneous conclusions with respect to regional homogeneity may be dr awn. The GLS procedure is shown to provide a general framework for a r eliable evaluation of parameter uncertainty as well as for an objectiv e appraisal of regional homogeneity. A comparison of the two different Bayesian T-year event estimators reveals that generally the simple li near estimator is adequate.