Multivariate models and inference

多元模型和推理

• 批准号: RGPIN-2021-02579
• 负责人: Joe, Harry
• 金额: $ 1.97万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765712
• 关键词: Multivariate; models; inference

In research studies in many areas, such as finance, measured variables do not follow the classical bell-shaped distribution individually and do not have dependence that can be multivariate Gaussian after transforms. In the past 10 years, the vine pair-copula construction has been the most flexible multivariate non-Gaussian distributions for applications. The vine pair-copula construction can handle measured variables that are continuous, discrete, binary or ordinal. In studies that required prediction of one (response) variable from explanatory variables and where the variables are simultaneously observed, the vine copula approach fits a joint distribution followed by inference from the conditional distribution of the response given the explanatory variables. Compare with classical methods of multiple regression, generalized linear models and survival regression, this approach allows prediction with models for flexible shapes for conditional quantiles and conditional variance as a function of the explanatory variables. The approach is especially useful for unbounded predictor spaces, as classical methods do not handled this situation well. With use of copulas in areas of applications involving risk, tail inference is important. To evaluate suitability of different models, we have developed tail-weighted measures of dependence as diagnostics in addition to the usual measures of central dependence. Our derivations are based on a tail form of copulas that allow for non-parametric estimation of joint tail (risk) probabilities and assess fits of parametric models. In some applications, we use latent variables similar to classical models, but with the use of copulas linking observed variables to latent variables to allow for more flexibility in tail dependence behaviour and better fits to multivariate data. The main objectives of some recent and proposed future research is to further develop multivariate models and inference/computing procedures for multivariate non-Gaussian response. With a larger number of variables, it is desirable to have multivariate models with parsimonious dependence structures and flexible tail behaviour. For predictions from conditional distributions after fitting a flexible copula, research is underway to compare models based on different vine copulas with models using machine learning methods; criteria include interpretability and out-of-sample performance. Variation selection is part of the model comparison.

在许多领域的研究中，例如金融，测量变量并不单独遵循经典的钟形分布，并且在变换后不具有可以是多元高斯的相关性。在过去的10年里，藤对Copula构造一直是最灵活的多元非高斯分布的应用。vine pair-copula构造可以处理连续、离散、二元或有序的测量变量。在需要从解释变量预测一个（响应）变量并且同时观察变量的研究中，vine copula方法拟合联合分布，然后从给定解释变量的响应的条件分布进行推断。与经典的多元回归、广义线性模型和生存回归方法相比，该方法允许对条件分位数和条件方差作为解释变量的函数的灵活形状的模型进行预测。该方法对于无界预测空间特别有用，因为经典方法不能很好地处理这种情况。在涉及风险的应用领域中使用copula，尾部推断是重要的。为了评估不同模型的适用性，我们已经开发了尾部加权的依赖性措施，除了通常的中央依赖性措施的诊断。我们的推导是基于尾形式的copula，允许联合尾部（风险）概率的非参数估计和评估参数模型的拟合。在某些应用中，我们使用类似于经典模型的潜变量，但使用连接观测变量到潜变量，以允许更灵活的尾部依赖行为和更好地拟合多变量数据。最近和未来研究的主要目标是进一步发展多变量非高斯响应的多变量模型和推理/计算程序。对于大量的变量，最好是具有简约的相关结构和灵活的尾部行为的多变量模型。对于在拟合灵活的copula之后从条件分布进行的预测，正在进行研究，以比较基于不同vine copula的模型与使用机器学习方法的模型;标准包括可解释性和样本外性能。变量选择是模型比较的一部分。