A distribution function based bandwidth selection method for kernel quantile estimation

The key problem in nonparametric frequency analysis of flood and droughts i s the estimation of the bandwidth parameter which defines the degree of smo othing. Most of the proposed bandwidth estimators have been based on the de nsity function rather than the cumulative distribution function or the quan tile that are the primary interest in frequency analysis. We propose a new bandwidth estimator derived from properties of quantile estimators. The est imator builds on work by Altman and Leger (1995). The estimator compared to the well-known method of least squares cross-validation (LSCV) using synth etic data generated from various parametric distributions used in hydrologi c frequency analysis. Simulations suggest that our estimator performs at le ast as well as, and in many cases better than, the method of LSCV. In parti cular, the use of the proposed plug-in estimator reduces bias in the estima tion as compared to LSCV. When applied to data sets containing observations with identical values, typically the result of rounding or truncation, the LSCV and most other techniques generally underestimates the bandwidth. The proposed technique performs very well in such situations. (C) 2001 Elsevie r Science B.V. All rights reserved.