Kernel flood frequency estimators: Bandwidth selection and kernel choice

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Abstract
Kernel density estimation methods have recently been introduced as viable and flexible alternatives to parametric methods for flood frequency estimation. Key properties of such estimators are reviewed in this paper. Attention is focused on the selection of the kernel function and the bandwidth. These are the parameters of the method. Existing techniques for kernel and bandwidth selection are applied to three situations: Gaussian data, skewed data (three‐parameter gamma), and mixture data. The intent was to investigate issues relevant to parameter estimation as well as to the likely performance of these methods with the small sample sizes typical in hydrology. Bandwidths chosen by minimizing a performance criterion related to the distribution function lead to much smaller mean square errors of tail probabilities than those chosen by cross‐validation methods designed for density estimation. However, this can lead to estimates that degenerate to the empirical distribution function, and hence to an unusable flood frequency curve. Variable bandwidths with heavy tailed kernels appear to do best. Kernel estimators are increasingly more competitive in terms of mean square error of estimate as the underlying distribution gets more complex.

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