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Notes:
add lprspdm package
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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