DATA-BASED CHOICE OF THE SMOOTHING PARAMETER FOR A KERNEL DENSITY ESTIMATOR

The problem of optimally choosing the smoothing parameter of a Fourier integral density estimator (FIE) is addressed. A new data-based method of so doing is shown to be related to, but an improvement over, the method of Davis (1981). It is shown that Davis' method does not lead to consistent estimation of certain, principally multimodal, densities. In a simulation study involving the bimodal mixture of two normal densities, the new method is seen to represent a substantial improvement.