Generalized method of L-moment estimation for stationary and nonstationary extreme value models

Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has been broadly used. To estimate the parameters of GEV distribution, the maximum likelihood estimation (MLE) and L-moment estimation (LME) methods have been primarily employed. For a better estimation using the MLE, several studies considered the generalized MLE (penalized likelihood or Bayesian) methods to cooperate with a penalty function or prior information for parameters. However, a generalized LME method for the same purpose has not been developed yet in the literature. We thus propose the generalized method of L-moment estimation (GLME) to cooperate with a penalty function or prior information. The proposed estimation is based on the generalized L-moment distance and a multivariate normal likelihood approximation. Because the L-moment estimator is more efficient and robust for small samples than the MLE, we reasonably expect the advantages of LME to continue to hold for GLME. The proposed method is applied to the stationary and nonstationary GEV models with two novel (data-adaptive) penalty functions to correct the bias of LME. A simulation study indicates that the biases of LME are considerably corrected by the GLME with slight increases in the standard error. Applications to US flood damage data and maximum rainfall at Phliu Agromet in Thailand illustrate the usefulness of the proposed method. This study may promote further work on penalized or Bayesian inferences based on L-moments.