Selection of bandwidth type and adjustment side in kernel density estimation over inhomogeneous backgrounds

This article identifies and compares four different methods for dealing with inhomogeneous backgrounds in kernel density estimation. The four methods result from combinations of two bandwidth types (fixed vs. adaptive) and two adjustment sides (site side vs. case side). The fixed and adaptive bandwidths employ different uniform bases in density calculation (spatial extent vs. population support). The adaptive bandwidth's strength lies in identifying spatial extents of density variation. It also produces values that are more comparable between locations and more stable statistically. When making adjustments to address the background, the site-side method makes the adjustment at each site for which the density value is to be estimated, and the case-side method makes the adjustment at each case location. Within a disease-mapping context, the former measures population at risk around each site and the latter measures around each disease case. The case-side adjustment is more justifiable in an application like disease mapping. It is also less sensitive to spatial details of the background (a favorable feature) and considerably more computationally efficient. Lung cancer data from Merrimack County, New Hampshire, USA, are used to demonstrate and compare the results from the four methods, leading to the conclusion that the case-side-adaptive-bandwidth method is most advantageous.