Dependence structure modeling: New directions and applications

依赖结构建模：新方向和应用

• 批准号: RGPIN-2019-06041
• 负责人: Bouezmarni, Taoufik
• 金额: $ 1.82万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738673
• 关键词: Dependence; structure; modeling; New; directions

Modeling the conditional and unconditional dependence is crucial in statistics and a misspecification of the dependence structure leads to a wrong conclusions. For example, the relationship between stock index returns and trading volume is important for prediction and testing Granger non-causality which a form of conditional independence.   In the literature, copula and regression functions are the most popular approches for modeling the relationship between variables. In this research program we will explore three directions of modeling the conditional and unconditional dependence.   Since Granger causality tests is a form of conditional independence, I have studied several tests of non-causality and when the null hypothesis is rejected, I have developed new measures of causality based on conditional copula and conditional distributions. The first direction of my proposal research program is devoted to the construction of tests of Granger non-causality and measures of causality with applications in finance and medicine among other fields. Over the next five years, I will explore and build a news non-causality tests based on exepctile, extremile regression and Asymptotically Distribution-Free (ADF) tests in regressions. Also, I will investigate some challenging, but very promising, novel ideas for measuring causality. A new package in R for my proposed tests in this direction will be developed. The second direction is related to my research on modeling of conditional and unconditional dependence using copula functions for incomplete data. Here, I will consider the incompleteness due to the right-censoring and length-biased sampling which is common in cross-sectional surveys.  Over the next five years, I will construct goodness-of-fit tests in order to select the adequate parametric copula of the right-censored length-biased data. In many situations, the dependence structure between two variables is influenced by a covariate. I will thus  investigate the conditional copula for modeling this conditional dependence structure and derive measures of the conditional dependence. Regression functions are usually used for modeling the relationship between a random variable (or vector) and a set of covariates. The third direction of my proposal is devoted to regression estimation using asymmetric error loss and copula functions. During the next five years, I will investigate a more general models for the regression function based on (a)symmetric error loss and copula. The mean, quantile and expectile regression models are a special cases of my proposed models. Also, to combine the robustness of the quantile regression and the efficiency of the expectile regression, I will develop a news  models for regression. A new package in R for all the proposed models will be an important objective to achieve.

对条件和无条件依赖性进行建模在统计数据中至关重要，并且依赖性结构的错误结论导致了错误的结论。例如，股票指数回报与交易量之间的关系对于一种有条件指数形式的预测和测试Granger非因果关系很重要。在文献中，副总结和回归函数是建模变量之间关系的最流行方法。在该研究计划中，我们将探讨对条件和无条件依赖性建模的三个方向。由于Granger休闲测试是一种有条件独立性的一种形式，因此我研究了几种非伴侣的测试，当拒绝零假设时，我已经基于条件copula和条件分布开发了新的休闲测量结果。我的提案研究计划的第一个方向致力于构建格兰杰的非因果关系测试，以及在金融和医学中的应用以及其他领域的应用。在接下来的五年中，我将基于回归中的exepctile，极端回归和不对称分配（ADF）测试进行探索和建立新闻非因果关系测试。另外，我将调查一些挑战但非常有希望的衡量休闲的新思想。将开发用于我在此方向上提议的测试的R中的新软件包。第二个方向与我对使用Copula函数的条件和无条件依赖性建模有关的研究有关。在这里，我将考虑由于右审查和长度偏置抽样而导致的不完整，这在横截面调查中很常见。在接下来的五年中，我将构建拟合优度测试，以便选择右键偏置数据的适当参数copula。在许多情况下，两个变量之间的依赖性结构受协变量的影响。因此，我将研究有条件的副本，以建模该条件依赖性结构并得出条件依赖性的衡量标准。回归函数通常用于建模随机变量（或向量）与一组协变量之间的关系。我的提案的第三个方向是使用不对称误差损失和副函数来进行回归估计。在接下来的五年中，我将根据（a）对称误差丢失和副群来研究一个更通用的回归函数模型。平均值，分位数和预期回归模型是我提出的模型的特殊情况。此外，为了结合分位数回归的鲁棒性和预期回归的效率，我将开发回归新闻模型。 R中的所有建议模型的新软件包将是实现的重要目标。