The selection of an appropriate nonstationary Generalized Extreme Value (GEV) distribution is frequently based on methods, such as Akaike information criterion (AIC), second-order Akaike information criterion (AICc), Bayesian information criterion (BIC) and likelihood ratio test (LRT). Since these methods compare all GEV-models considered within a selection process, the hypothesis that the number of candidate GEV-models considered in such process affects its own outcome has been proposed. Thus, this study evaluated the performance of these four selection criteria as function of sample sizes, GEV-shape parameters and different numbers candidate GEV-models. Synthetic series generated from Monte Carlo experiments and annual maximum daily rainfall amounts generated by the climate model MIROC5 (2006-2099; State of São Paulo-Brazil) were subjected to three distinct fitting processes, which considered different numbers of increasingly complex GEV-models. The AIC, AICc, BIC and LRT were used to select “the most appropriate” model for each series within each fitting process. BIC outperformed all other criteria when the synthetic series were generated from stationary GEV-models or from GEV-models allowing changes only in the location parameter (linear or quadratic). However, this latter method performed poorly when the variance of the series varied over time. In such cases, AIC and AICc should be preferred over BIC and LRT. The performance of all selection criteria varied with the different number of GEV-models considered in each fitting processes. In general, the higher the number of GEV-models considered within a selection process, the worse the performance of the selection criteria. In conclusion, the number of GEV-models to be used within a selection process should be set with parsimony.
Xavier, A. C. F., Blain, G. C., de Morais, M. V. B., & Sobierajski, G. da R. (2019). Selecting “the best” nonstationary generalized extreme value (Gev) distribution: On the influence of different numbers of GEV-models. Bragantia, 78(4), 606–621. https://doi.org/10.1590/1678-4499.20180408