KERNEL BANDWIDTH SELECTION FOR A FIRST-ORDER NONPARAMETRIC STREAMFLOWSIMULATION-MODEL

A new approach for streamflow simulation using nonparametric methods w as described in a recent publication (Sharma et al. 1997). Use of nonp arametric methods has the advantage that they avoid the issue of selec ting a probability distribution and can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to repre sent, in the probability structure of hydrologic variables such as str eamflow and precipitation. The nonparametric method used was kernel de nsity estimation, which requires the selection of bandwidth (smoothing ) parameters. This study documents some of the tests that were conduce d to evaluate the performance of bandwidth estimation methods for kern el density estimation. Issues related to selection of optimal smoothin g parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both reference to a Gaussian density and data based specifications are applied to estimate bandwidths for s amples from bivariate normal mixture densities. The three data based m ethods studied are Maximum Likelihood Cross Validation (MLCV), Least S quare Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modi fications for estimating optimal local bandwidths using MLCV and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with small samples. Of the gl obal bandwidth estimators compared, we found that MLCV and LSCV are be tter because they show lower variability and higher accuracy while Bia sed Cross Validation suffers from multiple optimal bandwidths for samp les from strongly bimodal densities. These results, of particular inte rest in stochastic hydrology where small samples are common, may have importance in other applications of nonparametric density estimation m ethods with similar sample sizes and distribution shapes.