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.

建模条件和无条件依赖关系在统计学中至关重要，依赖结构的错误指定会导致错误的结论，例如，股票指数收益与交易量之间的关系对于预测和测试格兰杰非因果关系很重要，格兰杰非因果关系是一种条件形式。​在文献中，联结函数和回归函数是对变量之间的关系进行建模的最流行的方法。在本研究计划中，我们将探索自格兰杰以来建模条件和非条件依赖性的三个方向。因果关系检验是条件独立性的一种形式，我研究了几种非因果关系检验，当零假设被拒绝时，我开发了基于条件联结和条件分布的新因果关系度量。我的提案研究计划的第一个方向是。致力于构建格兰杰非因果检验和因果关系测度及其在金融和医学等领域的应用。在接下来的五年里，我将探索和构建基于期望、极值回归的新闻非因果检验。此外，我将研究一些具有挑战性但非常有前途的测量因果关系的新想法，用于我在这个方向上提出的测试。与我使用联结函数对不完整数据进行条件和非条件依赖建模的研究相关，在这里，我将考虑由于横截面调查中常见的右审查和长度偏差抽样而导致的不完整性。未来五年，我将构建拟合优度检验，以便选择右删失长度偏差数据的适当参数联结函数。在许多情况下，两个变量之间的依赖结构会受到协变量的影响。研究用于建模此条件依赖性结构的条件联结并导出条件依赖性的度量通常用于对随机变量（或向量）和一组协变量之间的关系进行建模。提案致力于使用非对称误差损失和 copula 函数进行回归估计，在接下来的五年中，我将研究基于（a）对称误差损失和 copula 的更通用的回归函数模型。是我提出的模型的一个特例。此外，为了结合分位数回归的稳健性和期望回归的效率，我将为所有提出的模型开发一个新的 R 包。达到的目标。