Dependence structure modeling: New directions and applications

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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.