Nonparametric recursive regression estimation on Riemannian Manifolds

Salah Khardani and Anne Françoise Yao

Statistics & Probability Letters, 2022, vol. 182, issue C

Abstract: The considerations of this paper are restricted to random variables with values on Riemannian manifolds M and hence we propose a geometric framework to estimate their recursive regression function. Suppose we are given observations (Xi,Yi)i=1⋯n, where Xi∈M and Yi∈R. In this work we define and study a new estimator of the regression function on Riemannian Manifold M. Precisely, we employ a recursive version of the Nadaraya–Watson estimator on Riemannian Manifolds. Under some assumptions in Riemannian Manifolds data analysis, we study the properties of a recursive family kernels regression. The bias, variance are computed explicitly.

Keywords: Nonparametric regression; Recursive kernel estimator; Riemannian Manifolds; Bias; Variance (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2021.109274

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