Methods For Tracking Support Boundaries with Corners
Resource
Journal of Multivariate Analysis 97(8),1870-1893
Journal
Journal of Multivariate Analysis 97
Pages
1870-1893
Date Issued
2006
Date
2006
Author(s)
Hall, Peter
DOI
20060927121126023390
Abstract
In a range of practical problems the boundary of the support of a
bivariate distribution is of interest, for example where it describes a limit to e±-
ciency or performance, or where it determines the physical extremities of a spatially
distributed population in forestry, marine science, medicine, meteorology or geol-
ogy. We suggest a tracking-based method for estimating a support boundary when
it is composed of a ¯nite number of smooth curves, meeting together at corners.
The smooth parts of the boundary are assumed to have continuously turning tan-
gents & bounded curvature, & the corners are not allowed to be in¯nitely sharp;
that is, the angle between the two tangents should not equal ¼. In other respects,
however, the boundary may be quite general. In particular it need not be uniquely
de¯ned in Cartesian coordinates, its corners my be either concave or convex, and
its smooth parts may be neither concave nor convex. Tracking methods are well
suited to such generalities, & they also have the advantage of requiring relatively
small amounts of computation. It is shown that they achieve optimal convergence
rates, in the sense of uniform approximation.
Subjects
Bandwidth
boundary
corner
curvature
frontier
kernel method
local linear
nonparametric curve estimation
support
Type
journal article
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