Data Adaptive Estimation in Generalized Extreme Value Distribution

The generalized extreme value distribution(GEVD) is used to estimate the extreme events of natural phenomena. Likelihood based inference are discussed. Despite of having some pleasant features of maximum likelihood estimator it also has some disadvantages over small sample while dealing with negative shape parameter. This limitation has solved by imposing penalty function on likelihood equation. In this study we try to show that, instead of using an overall hyper-parameter to the penalized likelihood function. Data adaptive estimation procedure is introduced to selecting hyper parameter and to observe the performance of the penalty functions as well as with maximum likelihood estimator. Some of the rainfall data sets of South Korea are discussed.