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.
SynopsisVisual Analogue Scales (VAS) provide a simple technique for measuring subjective experience. They have been established as valid and reliable in a range of clinical and research applications, although there is also evidence of increased error and decreased sensitivity when used some subject groups. Decisions concerned with the choice of scoring interval, experimental design, and statistical analysis for VAS have in some instances been based on convention, assumption and convenience, highlighting the need for more comprehensive assessment of individual scales if this versatile and sensitive measurement technique is to be used to full advantage.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.