Level set and density estimation on manifolds

Alejandro Cholaquidis, Ricardo Fraiman and Leonardo Moreno

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: We tackle the problem of the estimation of the level sets Lf(λ) of the density f of a random vector X supported on a smooth manifold M⊂Rd, from an iid sample of X. To do that we introduce a kernel-based estimator fˆn,h, which is a slightly modified version of the one proposed in Rodríguez-Casal and Saavedra-Nieves (2014) and proves its a.s. uniform convergence to f. Then, we propose two estimators of Lf(λ), the first one is a plug-in: Lfˆn,h(λ), which is proven to be a.s. consistent in Hausdorff distance and distance in measure, if Lf(λ) does not meet the boundary of M. While the second one assumes that Lf(λ) is r-convex, and is estimated by means of the r-convex hull of Lfˆn,h(λ). The performance of our proposal is illustrated through some simulated examples. In a real data example we analyze the intensity and direction of strong and moderate winds.

Keywords: Density estimation; Level set estimation; Riemannian manifold data (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104925

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