Empirical and sequential empirical copula processes under serial dependence
Empirical and sequential empirical copula processes under serial dependence
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DOI：
10.1016/j.jmva.2013.04.003
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发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Axel Bücher;S. Volgushev
中科院分区：
文献类型：
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作者：
Axel Bücher;S. Volgushev
经验和序列经验copula过程在copula的统计推断中起着核心作用。然而，正如Johan Segers [J. Segers，Asymptotics of empirical copula processes under non-restricted smoothness assumptions，Bernoulli 18（3）（2012）764-782]所指出的那样，迄今为止研究这些过程所依据的通常假设限制性太强。在本文中，我们提供了一个统一的方法来分析经验和序列的经验copula过程，绕过这些限制性的假设，在一个非常一般的设置。特别是，我们的方法可以很容易地分析Copula过程和适当的自举近似设置顺序相关的数据。一个特别有用的发现是，某些连续的经验copula过程收敛，没有任何光滑性假设的copula。
Empirical and sequential empirical copula processes play a central role for statistical inference on copulas. However, as pointed out by Johan Segers [J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (3) (2012) 764–782] the usual assumptions under which these processes have been studied so far are too restrictive. In this paper, we provide a unified approach to the analysis of empirical and sequential empirical copula processes that circumvents those restrictive assumptions in a very general setting. In particular, our methods allow for an easy analysis of copula processes and appropriate bootstrap approximations in the setting of sequentially dependent data. One particularly useful finding is that certain sequential empirical copula processes converge without any smoothness assumptions on the copula.