|
Notes:
add lprspdm package, see Ying Yuan, Hongtu Zhu, Weili Lin, J. S. Marron (2011). Local
Polynomial Regression for Symmetric Positive
Definite Matrices. JRSSB
Local polynomial regression has received extensive attention for
the
nonparametric estimation of regression functions when both the
response
and the covariate are in Euclidean space. However, little has been
done
when the response is in a Riemannian manifold. We develop an
intrinsic
local polynomial regression estimate for the analysis of
symmetric
positive definite (SPD) matrices as responses that lie in a
Riemannian
manifold with covariate in Euclidean space. The primary motivation
and
application of the proposed methodology is in computer vision
and
medical imaging. We examine two commonly used metrics, including
the
trace metric and the Log- Euclidean metric on the space of SPD
matrices.
For each metric, we develop a cross-validation bandwidth
selection
method, derive the asymptotic bias, variance, and normality of
the
intrinsic local constant and local linear estimators, and compare
their
asymptotic mean square errors
Changes:
|
