Level set and density estimation on manifolds

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