k-Nearest neighbor density estimation on Riemannian Manifolds

Details k-Nearest neighbor density estimation on Riemannian Manifolds k-Nearest neighbor density estimation on Riemannian Manifolds

2011-06-23

arxiv.org/abs/1106.4763v1

Mathematics

Statistics Theory

17 pages, 5 figures

Scientific paper

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.

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