| Variable bandwidth kernel density estimators increase the window width at low densities and decrease it where data concentrate. This represents an improvement over the fixed bandwidth kernel density estimators. In this article, we explore the use of one implementation of a variable kernel estimator in conjunction with several rules and procedures for bandwidth selection applied to several real datasets. The considered examples permit us to state that when working with tens or a few hundreds of data observations, least-squares cross-validation bandwidth rarely produces useful estimates; with thousands of observations, this problem can be surpassed. Optimal bandwidth and biased cross-validation (BCV), in general, oversmooth multimodal densities. The... |
