Dependence structure modeling: New directions and applications

条件依赖和无条件依赖的建模是统计学中的关键问题，而对依赖结构的错误描述会导致错误的结论。例如，股票指数收益率与交易量之间的关系对于预测和检验条件独立性的格兰杰非因果关系具有重要意义。 在文献中，Copula和回归函数是最流行的建模变量之间的关系的方法。在这个研究计划中，我们将探讨三个方向的建模的条件和无条件的依赖。 由于格兰杰因果关系检验是一种条件独立性的形式，我研究了几种非因果关系的检验，当原假设被拒绝时，我开发了基于条件copula和条件分布的新的因果关系度量。我的建议研究计划的第一个方向是致力于建设的格兰杰非因果关系和因果关系的措施，在金融和医学等领域的应用测试。在接下来的五年里，我将探索和建立一个基于极端、极端回归和回归中的无渐近分布（ADF）检验的新闻非因果检验。此外，我将研究一些具有挑战性，但非常有前途的，新颖的想法来衡量因果关系。将开发一个新的R包，用于我在这个方向上提出的测试。 第二个方向与我的研究有关的建模的条件和无条件依赖使用Copula函数的不完整数据。在这里，我将考虑由于横截面调查中常见的右删失和长度偏差抽样而导致的不完整性。 在接下来的五年里，我将构造拟合优度检验，以选择适当的参数copula的右删失长度偏置数据。在许多情况下，两个变量之间的依赖结构受到协变量的影响。因此，我将调查的条件Copula建模这种条件依赖结构，并得出措施的条件依赖。回归函数通常用于建模随机变量（或向量）和协变量集之间的关系。我的建议的第三个方向是致力于使用非对称误差损失和copula函数的回归估计。在接下来的五年里，我将研究基于对称误差损失和copula的回归函数的更一般的模型。均值、分位数和期望回归模型是本文所提出模型的一个特例。同时，为了联合收割机分位数回归的稳健性和期望回归的有效性，我将建立一个新的回归模型。在R中为所有提出的模型提供一个新的包将是一个重要的目标。

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.