单峰密度的渐近独立性
Asymptotic independence for unimodal densities
摘要：
随机向量的分量的渐近独立性是在许多应用中使用的概念。用分布函数（dfs）给出了检验渐近独立性的标准准则。Dfs很少以显式形式提供，特别是在多变量情况下。通常我们给出密度的形式，或者通过数据云的形状，可以获得密度水平集的渐近形状的良好几何图像。本文利用这种渐近形状建立了轻尾密度渐近独立的一个简单的充分条件。这个条件扩展了Sibuya关于高斯密度的渐近独立性的经典结果。
英文摘要：
Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (dfs). Dfs are rarely available in an explicit form, especially in the multivariate case. Often we are given the form of the density or, via the shape of the data clouds, one can obtain a good geometric image of the asymptotic shape of the level sets of the density. This paper establishes a simple sufficient condition for asymptotic independence for light-tailed densities in terms of this asymptotic shape. This condition extends Sibuya's classic result on asymptotic independence for Gaussian densities.
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