A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation

Abstract

SUMMARY We present a new method for data‐based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the existing literature. These methods are based on choosing the bandwidth to (approximately) minimize good quality estimates of the mean integrated squared error. The key to the success of the current procedure is the reintroduction of a non‐stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance.

Episodic Quaternary volcanism in France and Germany

“…4) are a consequence of these ad hoc modifications to this method made to take into account the lack of present-day volcanism in our study areas. In addition, the degree to which the data has been smoothed by the selected bandwidths-one for each data point-has been solved rather subjectively to be either twothirds of the Sheather and Jones (1991) automatically chosen bandwidth for data without measurement error or 1.25 times the standard deviation, whichever is the larger.…”

Simple boundary correction for kernel density estimation

“…As a first approximation, one can clearly use a procedure which ignores boundary considerations, and this we did, using Sheather and Jones' (1991) method, in Fig. 7.…”

Nonparametric Estimation

“…Sheather (1983) suggested another approach but later showed that bias is a concern and derived a method for getting better results (Sheather 1986). More recently, Sheather and Jones (1991) investigated other methods aimed at minimizing a kernel-based estimate of MISE. But perhaps a more basic issue is whether plug-in methods, such as those just cited, should be used over what are called classic methods, which include cross-validation, Mallow's C p criterion, and Akaike's information criterion (AIC).…”