The R package kerdiest has been designed for computing kernel estimators of the distribution function and other related functions. Because of its usefulness in real applications, the bandwidth parameter selection problem has been considered, and a cross-validation method and two of plug-in type have been implemented. Moreover, three relevant functions in nature hazards have also been programmed. The package is completed with two interesting data sets, one of geological type (a complete catalogue of the earthquakes occurring in the northwest of the Iberian Peninsula) and another containing the maximum peak flow levels of a river in the United States of America.

This paper proposes a new nonparametric estimate of the conditional mode. This mode estimate is obtained from kernel smoothing of the first derivative of the conditional density function with location adaptive bandwidth. We give the rates of convergence of this estimate under general dependence conditions on the sample that make our results valid for nonparametric prediction of time series. As a by-products, we also get rate of convergence of the usual mode of a density function under dependence, and we give some extensions to local bandwidth of recent results on kernel estimation under mixing conditions.

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Abstract: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.

Bandwidth selection, kernel smoothing, mixing, partial linear models, 62G05, 62G20, 62M10,