Projection estimators of Pickands dependence functions
Projection estimators of Pickands dependence functions
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DOI：
10.1002/cjs.5550360303
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发表时间：
2008-09-01
影响因子：
0.6
通讯作者：
Segers, Johan
中科院分区：
文献类型：
--
作者：
Fils-Villetard, Amelie;Guillou, Armelle;Segers, Johan
考虑极值copula函数的Pickands相依函数的内禀估计的构造。它们展示了如何修改任意初始估计以满足所需的形状约束。他们的解决方案包括将此估计量投影到Pickands函数的空间中，该空间形成希尔伯特空间的闭凸子集。由于解不是显式的，他们用有限维子集的筛子代替了这个函数参数空间。他们建立了投影估计量的渐近分布及其有限维近似，由此得出结论，投影估计量至少与初始估计量一样有效。
The authors consider the construction of intrinsic estimators for the Pickands dependence function of an extreme-value copula. They show how an arbitrary initial estimator can be modified to satisfy the required shape constraints. Their solution consists in projecting this estimator in the space of Pickands functions, which forms a closed and convex subset of a Hilbert space. As the solution is not explicit, they replace this functional parameter space by a sieve of finite-dimensional subsets. They establish the asymptotic distribution of the projection estimator and its finite-dimensional approximations, from which they conclude that the projected estimator is at least as efficient as the initial one.