Gradient-Boosted Generalized Linear Models for Conditional Vine Copulas

IF 1.5 3区 环境科学与生态学 Q4 ENVIRONMENTAL SCIENCES
Environmetrics Pub Date : 2024-12-05 DOI:10.1002/env.2887
David Jobst, Annette Möller, Jürgen Groß
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引用次数: 0

Abstract

Vine copulas are flexible dependence models using bivariate copulas as building blocks. If the parameters of the bivariate copulas in the vine copula depend on covariates, one obtains a conditional vine copula. We propose an extension for the estimation of continuous conditional vine copulas, where the parameters of continuous conditional bivariate copulas are estimated sequentially and separately via gradient-boosting. For this purpose, we link covariates via generalized linear models (GLMs) to Kendall's τ $$ \tau $$ correlation coefficient from which the corresponding copula parameter can be obtained. In a second step, an additional covariate deselection procedure is applied. The performance of the gradient-boosted conditional vine copulas is illustrated in a simulation study. Linear covariate effects in low- and high-dimensional settings are investigated separately for the conditional bivariate copulas and the conditional vine copulas. Moreover, the gradient-boosted conditional vine copulas are applied to the multivariate postprocessing of ensemble weather forecasts in a low-dimensional covariate setting. The results show that our suggested method is able to outperform the benchmark methods and identifies temporal correlations better. Additionally, we provide an R-package called boostCopula for this method.

Abstract Image

条件藤连的梯度增强广义线性模型
Vine copula是使用二元copula作为构建块的灵活依赖模型。如果双变量藤联中的参数依赖于协变量,则得到一个条件藤联。我们提出了一种对连续条件藤连估计的扩展,其中连续条件二元连的参数通过梯度增强分别被估计。为此,我们通过广义线性模型(GLMs)将协变量与Kendall τ $$ \tau $$相关系数联系起来,从中可以获得相应的copula参数。在第二步中,应用额外的协变量取消选择过程。通过仿真研究说明了梯度增强条件藤连的性能。本文分别研究了低维和高维条件下的双变量联系式和条件蔓生联系式的线性协变量效应。此外,本文还将梯度增强的条件藤copuls应用于低维协变量集合天气预报的多变量后处理。结果表明,本文提出的方法能够更好地识别时间相关性,优于基准方法。此外,我们为该方法提供了一个名为boostCopula的r包。
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来源期刊
Environmetrics
Environmetrics 环境科学-环境科学
CiteScore
2.90
自引率
17.60%
发文量
67
审稿时长
18-36 weeks
期刊介绍: Environmetrics, the official journal of The International Environmetrics Society (TIES), an Association of the International Statistical Institute, is devoted to the dissemination of high-quality quantitative research in the environmental sciences. The journal welcomes pertinent and innovative submissions from quantitative disciplines developing new statistical and mathematical techniques, methods, and theories that solve modern environmental problems. Articles must proffer substantive, new statistical or mathematical advances to answer important scientific questions in the environmental sciences, or must develop novel or enhanced statistical methodology with clear applications to environmental science. New methods should be illustrated with recent environmental data.
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