New Gradient Methods for Bandwidth Selection in Bivariate Kernel Density Estimation

The bivariate kernel density estimator is fundamental in data smoothing methods especially for data exploration and visualization purposes due to its ease of graphical interpretation of results. The crucial factor which determines its performance is the bandwidth. We present new methods for bandwidth selection in bivariate kernel density estimation based on the principle of gradient method and compare the result with the biased cross-validation method. The results show that the new methods are reliable and they provide improved methods for a choice of smoothing parameter. The asymptotic mean integrated squared error is used as the measure of performance of the new methods.