Lattice-based methods for regression and density estimation on complicated multidimensional regions

• Published in: Environmental and ecological statistics Vol. 27; no. 3; pp. 571 - 589
• Main Authors: Barry, Ronald P., McIntyre, Julie
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-09-2020; Springer Nature B.V
• Subjects: Biomedical and Life Sciences; Boundaries; Chemistry and Earth Sciences; Computer Science; Cylinders; Density; Domains; Ecology; Health Sciences; Life Sciences; Math. Appl. in Environmental Science; Medicine; Multidimensional methods; Nonparametric statistics; Physics; Statistics for Engineering; Statistics for Life Sciences; Theoretical Ecology/Statistics; Diffusion; Kernel estimation; Nonparametric smoothing
• ISSN: 1352-8505; 1573-3009
• DOI: 10.1007/s10651-020-00459-z

This paper illustrates the use of diffusion kernels to estimate smooth density and regression functions defined on highly complex domains. We generalize the two-dimensional lattice-based estimators of Barry and McIntyre (
2011
) and McIntyre and Barry (
2018
) to estimate any function defined on a domain that may be embedded in
R
d
,
d
≥
1
. Examples include function estimation on the surface of a sphere, a sphere with boundaries and holes, a sphere over multiple time periods, a linear network, the surface of cylinder, a three-dimensional volume with boundaries, and a union of one- and two-dimensional subregions.