An evaluation of likelihood-based bandwidth selectors for spatial and spatiotemporal kernel estimates

ABSTRACT

Spatial point pattern data sets are commonplace in a variety of different research disciplines. The use of kernel methods to smooth such data is a flexible way to explore spatial trends and make inference about underlying processes without, or perhaps prior to, the design and fitting of more intricate semiparametric or parametric models to quantify specific effects. The long-standing issue of ‘optimal’ data-driven bandwidth selection is complicated in these settings by issues such as high heterogeneity in observed patterns and the need to consider edge correction factors. We scrutinize bandwidth selectors built on leave-one-out cross-validation approximation to likelihood functions. A key outcome relates to previously unconsidered adaptive smoothing regimens for spatiotemporal density and multitype conditional probability surface estimation, whereby we propose a novel simultaneous pilot-global selection strategy. Motivated by applications in epidemiology, the results of both simulated and real-world analyses suggest this strategy to be largely preferable to classical fixed-bandwidth estimation for such data.

KEYWORDS:

• Cross-validation
• density estimation
• geographical epidemiology
• optimal bandwidth
• point pattern

2010 Mathematics Subject Classifications:

• 62H11
• 62G07

Acknowledgments

All computations and analyses were performed in the R programming environment [41] using the contributed packages spatstat [42] and sparr [43]. Simulation study design was aided by the spagmix package [44], and the 3D plots were created using functionality of the rgl [45] and misc3d [46] packages.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Tilman M. Davies http://orcid.org/0000-0003-0565-1825

Additional information

Funding

The first author acknowledges partial financial support from the Royal Society of New Zealand, Marsden Fast-start grant 15-UOO-092.