On bandwidth selection for nonparametric estimation in flood frequency analysis

Nonparametric estimation of the distribution function of the annual maxima (AM) flood series is considered. In practice, the good behaviour of the nonparametric estimators depends heavily on the smoothing parameter or bandwidth. Nowadays, there exist only two (optimal under a mathematical point of view) bandwidth parameter selection methods in nonparametric distribution function estimation: cross-validation and plug-in. In this work, the cross-validation procedure of Bowman et al. [Bowman A, Hall P, Prvan T. 1998. Bandwidth selection for the smoothing of distribution functions. Biometrika 85: 799-808] is analysed. A simulation study checks the finite sample performance of the corresponding estimators, and a comparison of this method with a parametric procedure (the fitting of a extreme value distribution) is done with flow data of Salt River (AZ, USA). Along this work, we point out some common mistakes made in some papers dealing with statistical problems in hydrology, such as the use of the empirical distribution function instead of the observed data, or the bandwidth parameter selection by means of some method designed for nonparametric density estimation. Copyright (C) 2010 John Wiley & Sons, Ltd.