论文标题
水平设置和歧管上的密度估计
Level set and density estimation on manifolds
论文作者
论文摘要
我们解决了从X的IID示例中支持的随机矢量X的级别集合l_f（λ）的估计值L_F（λ）的问题。为此，我们介绍了基于内核的估算仪f^n，h，这是对[45]的A. A. S. S. S. S. S. S. S. S. S.均匀收敛到f。然后，我们提出了两个l f（λ）的估计值，第一个是插件：l f^n，h（λ），被证明为A.S.如果l f（λ）不符合m的边界，则在Hausdorff距离和度量中的距离一致。第二个假设L F（λ）是R-Convex，并且通过L f^n，H（λ）的R-Convex船体进行估计。通过一些模拟示例说明了我们的提案的表现。在一个真实的数据示例中，我们分析了强风的强度和方向。
We tackle the problem of the estimation of the level sets L_f(λ) of the density f of a random vector X supported on a smooth manifold M\subsetR^d , from an iid sample of X. To do that we introduce a kernel-based estimator f^n,h , which is a slightly modified version of the one proposed in [45], and proves its a.s. uniform convergence to f . Then, we propose two estimators of L f (λ), the first one is a plug-in: L f^n,h (λ), which is proven to be a.s. consistent in Hausdorff distance and distance in measure, if L f(λ) does not meet the boundary of M . While the second one assumes that L f(λ) is r-convex, and is estimated by means of the r-convex hull of L f^n,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.
