论文标题
从马尔可夫内核角度来看
Total positivity of copulas from a Markov kernel perspective
论文作者
论文摘要
两个随机变量之间的基本依赖结构可以通过多种方式描述。这包括检查某些依赖性特性，例如较低的尾巴降低（LTD），随机增加度（SI）或阶2的总阳性，后者通常考虑用于copula（TP2）或（如果存在）其密度（D-TP2）。 In the present paper we investigate total positivity of order 2 for a copula's Markov kernel (MK-TP2 for short), a positive dependence property that is stronger than TP2 and SI, weaker than d-TP2 but, unlike d-TP2, is not restricted to absolutely continuous copulas, making it presumably the strongest dependence property defined for any copula (including those with a singular part such as Marshall-Olkin copulas).我们检查了不同copula家族的MK-TP2特性，其中包括阿基米德群岛的类别和极值的高价值。特别是，我们表明，在阿基米氏菌的类别中，依赖性属性SI和MK-TP2等效。
The underlying dependence structure between two random variables can be described in manifold ways. This includes the examination of certain dependence properties such as lower tail decreasingness (LTD), stochastic increasingness (SI) or total positivity of order 2, the latter usually considered for a copula (TP2) or (if existent) its density (d-TP2). In the present paper we investigate total positivity of order 2 for a copula's Markov kernel (MK-TP2 for short), a positive dependence property that is stronger than TP2 and SI, weaker than d-TP2 but, unlike d-TP2, is not restricted to absolutely continuous copulas, making it presumably the strongest dependence property defined for any copula (including those with a singular part such as Marshall-Olkin copulas). We examine the MK-TP2 property for different copula families, among them the class of Archimedean copulas and the class of extreme value copulas. In particular we show that, within the class of Archimedean copulas, the dependence properties SI and MK-TP2 are equivalent.
