Formal statistical tools for the dependence modeling of environmental data

在环境问题和气候变化方面做出明智的决定对未来几年的世界决策者至关重要。因此，必须向公众提供基于对自然现象透彻理解的坚实论据。从这个角度来看，用正式统计方法分析复杂的环境数据是必须迅速发展的一个关键因素。 由于一个给定的环境现象通常涉及几个随机变量，有一个明确的兴趣，为他们的关系的研究。为此，一个好的策略是依靠成熟的copula方法。然而，尽管在过去的15年里，在适用于Copula的统计推断方面取得了许多进展，但现有的工具必须加以改进，以应对现在可用的环境数据日益复杂的情况。从这一前提出发，本研究计划的目的是在Copula依赖建模的三个一般方面取得重大进展，这将对复杂环境数据的分析产生影响： (A)由于一个适当的依赖结构的正式选择是理解一个自然现象的关键，全新的统计推断程序的基础上copula特征函数将允许测试的许多类型的假设，涉及copula; (B)由于现有的copula模型的灵活性在变量数量变大时受到限制，因此将考虑为高维背景创建模型和统计工具，重点是空间统计、多元回归和新兴的大数据领域的应用; (C)由于气候变化检测/建模工具通常假设突变的不切实际的情景，因此将开发基于新的渐变依赖模型的新的统计检验和建模工具，用于分析气候时间序列。 此外，为了促进新方法的可重复性和传播，编码程序将通过My Matlab网页提供给整个研究社区。 将与本提案一起开发的方法工具通常是非参数和半参数的，这是因为一个感兴趣的人口的copula不能从样本中观察到，而只能间接地从等级中观察到。新的统计方法的正式理由，然后将需要在非参数统计和大样本的经验过程技术的知识和新的发展，以获得的一致性和弱收敛的秩统计，以及适当的适应reservation技术的有效性，除其他事项外。

Smart decisions on environmental issues and climate changes are crucial for the decision makers of the world in the coming years. It is thus important that solid arguments based on a thorough understanding of natural phenomena are available for public use. From this perspective, the analysis of complex environmental data with formal statistical methods is a key element that must be rapidly developed. Since a given environmental phenomenon typically involve several random variables, there is a clear interest for the study of their relationships. To this end, a good strategy is to rely on the well-established copula approach. However, although many advances in statistical inference adapted to copulas took place in the last fifteen years, the available tools must be improved to deal with the growing complexity of the environmental data that are now available. Setting out from this premise, this research program aims at making significant advances in three general aspects of dependence modeling with copulas that will have an impact on the analysis of complex environmental data: (A) Because the formal choice of an appropriate dependence structure is crucial for the understanding of a natural phenomenon, brand new statistical inference procedures based on copula characteristic functions will allow for the testing of many types of hypotheses involving copulas; (B) Since the flexibility of the available copula models is limited when the number of variables gets large, the creation of models and statistical tools for high-dimensional contexts will be considered, with a focus on applications in spatial statistics, multivariate regression, and the emerging field of Big Data; (C) Because the tools for the detection/modeling of climatic changes generally assume an unrealistic scenario of an abrupt change, new statistical tests and modeling tools based on a novel gradual-change dependence model will be developed for the analysis of climatic time series. Moreover, in order to promote the reproducibility and dissemination of the new methodologies, the coded procedures will be made available to the entire research community via My Matlab webpage. The methodological tools that will be developed with this proposal are typically nonparametric and semi-parametric, a consequence of the fact that the copula of a population of interest is not observable from the sample, but only indirectly from the ranks. The formal justification of the new statistical methods will then require knowledge and new developments in nonparametric statistics and large-sample empirical processes techniques to derive the consistency and weak convergence of rank statistics, as well as for the validity of suitably adapted resampling techniques, among other things.