This research area focuses on the development of multivariate copula-based models and inference procedures for non-normal multivariate/longitudinal response data.

Multivariate/longitudinal response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences. Data from these application areas have different dependence structures including features such as tail dependence or negative dependence. Studying dependence among multivariate response data is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. For example, most existing models assume rigid margins of the same form (e.g., Gaussian, Student, exponential, Gamma, Poisson, etc.) or limited dependence (e.g., tail independence, positive dependence, etc.).

To solve this problem we use copulas (multivariate distributions with uniform margins). Copulas are unified way to model multivariate response data, as they account for the dependence structure and provide a flexible representation of the multivariate distribution. They allow for general dependence modelling, different from assuming simple linear correlation structures and normality.Copulas enable you to break the model building process into two separate steps:

1. Choice of arbitrary marginal distributions:

• They could take different forms;
• They could involve covariates.

2. Choice of an arbitrary copula function (dependence structure).

That makes them particularly well suited to the aforementioned application areas.

We have links and collaborate with key individuals in the area, e.g. Prof Harry Joe (University of British Columbia); Prof Haijun Li (Washington State University); Prof Christian Genest (McGill University).

We are committed to making our methods available to the research community. For example, we have released the package weightedScores for the weighted scores method for regression models with dependent data in the OpenSource R project for statistical computing.

#### References

1. Nikoloulopoulos, A.K. On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood. Journal of Statistical Planning and Inference, 143:1923-1937, 2013.
2. Nikoloulopoulos, A.K.  Copula-based models for  multivariate discrete response data. In Durante, F., Hardle, W. and Jaworski, P. (Eds.), Copulae in Mathematical and Quantitative Finance, Lecture Notes in Statistics, Springer, pp. 231-249, 2013.
3. Genest, C., Nikoloulopoulos, A.K., Rivest, L.-P. and Fortin, M. Predicting dependent binary outcomes through logistic regressions and meta-elliptical copulas. Brazilian Journal of Probability and Statistics, 27:265-284, 2013.
4. Nikoloulopoulos, A.K., Joe, H. and Li, H. Vine copulas with asymmetric tail dependence and applications to financial return data Computational Statistics and Data Analysis, 56:3659-3673, 2012.
5. Nikoloulopoulos, A.K. Comment on `Two-dimensional toxic dose and multivariate logistic regression, with application to decompression sickness' by Li, J. and Wong, W.K. Biostatistics, 13: 1-3, 2012.
6. Nikoloulopoulos, A.K., Joe, H. and Chaganty, N.R. Weighted scores method for regression models with dependent data. Biostatistics, 12: 653–665, 2011.
7. Nikoloulopoulos, A.K. and Karlis D.  Regression in a copula model for bivariate count data. Journal of Applied Statistics, 37: 1555-1568, 2010.
8. Nikoloulopoulos, A.K. and Karlis, D. Modeling multivariate count data using copulas. Communications in Statistics-Simulation and Computation, 39: 172-187, 2010.
9. Joe, H., Li, H. and Nikoloulopoulos, A.K. Tail dependence functions and vine copulas. Journal of Multivariate Analysis, 101:252-270, 2010.
10. Nikoloulopoulos, A.K. and Karlis, D. Finite normal mixture copulas for multivariate discrete data modeling. Journal of Statistical Planning and Inference, 139:3878-3890, 2009.
11. Nikoloulopoulos, A.K., Joe, H. and Li, H. Extreme value properties of multivariate t copulas.Extremes, 12:129-148, 2009.
12. Nikoloulopoulos, A.K. and Karlis, D. Multivariate logit copula model with an application to dental data. Statistics in Medicine, 27:6393-6406, 2008.
13. Nikoloulopoulos, A.K. and Karlis, D.  Copula model evaluation based on parametric bootstrap. Computational Statistics and Data analysis, 52:3342-3353, 2008.
14. Nikoloulopoulos, A.K. and Karlis, D. Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited. Environmetrics, 19:251-269, 2008.