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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
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