A0931
Title: A semiparametric approach in estimating sample maximum distribution
Authors: Taku Moriyama - Yokohama City University (Japan) [presenting]
Abstract: A semiparametric approach is considered in estimating sample maximum distribution in iid settings. The sample maximum distribution is approximated by the generalized extreme value distribution. However, the convergence rate of the fitting estimator heavily depends on the tail index and gets slow as the index tends to zero. First, a fully nonparametric approach is introduced as an alternative approach and reports its asymptotic properties. The convergence rate of the nonparametric estimator with the optimal regularization parameter does not depend on the tail index under regularity conditions. Hence, the nonparametric approach outperforms the fitting estimator theoretically and numerically for distributions with the tail index around zero. On the other hand, the numerical accuracy of the nonparametric estimator is very poor for distributions with a tail index far from zero. A semiparametric mixture of the two approaches is proposed to develop a new approach complementing each other. Cross-validation and maximum-likelihood methods are provided for the mixing ratio selection, and reduction in computational cost is also discussed. The simulation experiment results and discusses the semiparametric estimator's numerical properties estimator are discussed.
