论文标题
一个新的平滑库氏家族，任意不规则密度
A new family of smooth copulas with arbitrarily irregular densities
论文作者
论文摘要
众所周知，Copulas可以满足许多规律性的特性，因此，人们可能会认为，当它们存在时，它们本身就承认了一定程度的规律性。我们表明，通常通过建造一个广泛的小家族来承认几乎不能被认为是规律的，这是不正确的。副群密度是由单位间隔支撑的任意单变量密度构建的，我们以示例表明，副群密度可以从基本的单变量密度继承病理行为。特别是，我们构建了一个非平凡的单变量密度，该密度在单位间隔的每个开放组中都无限，并表明它诱导了一个copula密度，该密度无处不在，但在单位HyperCube的每个社区中都无限。然而，我们所有的Copulas都享有吸引人的平滑性能。
Copulas are known to satisfy a number of regularity properties, and one might therefore believe that their densities, when they exist, admit a certain degree of regularity themselves. We show that this is not true in general by constructing a broad family of copulas which admit densities that can hardly be considered regular. The copula densities are constructed from arbitrary univariate densities supported on the unit interval, and we show by example that the copula densities can inherit pathological behaviour from the underlying univariate densities. In particular, we construct a nontrivial univariate density which is unbounded in every open set of the unit interval, and show that it induces a copula density which is finite everywhere but unbounded in every neighborhood of the unit hypercube. Nevertheless, all of our copulas are shown to enjoy attractive smoothness properties.
