Fully Funded Studentship: Dependence modelling and construction of multivariate copulas

Fully Funded Studentship: Dependence modelling and construction of multivariate copulas

School: Computing Sciences

Supervisor(s): Dr Aristidis K. Nikoloulopoulos (A.Nikoloulopoulos@uea.ac.uk)

Application Deadline: May 28th 2010 12th March 2010; 29th January 2010; 4th December 2009

Funding is available for UK/EU students. Funding awarded for this project will cover tuition fees
and stipend for UK students. EU students may be eligible for full funding, or tuition fees only,
depending on the funding source. International students will not be eligible for this funding
however they are still welcome to apply for this project but would have to find alternative funding.

Description:

This project will focus on dependence modelling and construction of multivariate copulas for
non-normal multivariate/longitudinal response data. There are two goals for constructing
multivariate copulas for dependence modelling: For continuous data there is a need for copula
families with a flexible range of lower/upper tail dependence. Tail dependence and conditional tail
dependence functions describe, respectively, the tail probabilities and conditional tail
probabilities of a copula at various relative scales. The extremal dependence behaviour of various
multivariate distributions will be examined and their extreme value limiting copulas will be derived
using tail dependence functions in order to derive new copula families with a flexible range of
lower/upper tail dependence. For discrete data there is a need for copula families with a wide range
of dependence, including negative dependence and computationally feasible form of the cumulative
distribution function (cdf). Usually we have to trade off between models via simple parametric
families of copulas with limited dependence (e.g. only positive association) and models via copulas
with flexible dependence but computational intractabilities. For example, the elliptical copulas
provide a wide range of flexible dependence, but lack applicability for multivariate discrete data
because of multidimensional integration. We will try to overcome these problems by (a) the
definition of a parametric family of copulas which has simple form for its cdf while allowing for
negative dependence among the variables, (b) special estimation methods in order to overcome the
complexities imposed by the elliptical copula-based models. The use of composite likelihood methods
can be a potential path towards simplifications of such models.

References


Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall, London.

Joe, H., Li, H. and Nikoloulopoulos, A.K. (2009) Tail dependence functions and vine copulas. Journal
of Multivariate Analysis, 101:252-270.

Nikoloulopoulos, A.K., Joe, H. and Li, H. (2009) Extreme value properties of multivariate t copulas.
Extremes, 12:129-148.

Nikoloulopoulos, A.K. and Karlis, D. (2009) Finite normal mixture copulas for multivariate discrete
data modeling.

Zhao, Y. and Joe,H. (2005) Composite likelihood estimation in multivariate data analysis. Canadian
Journal of Statistics, 33:335-356.

Research Areas: Applied Mathematics

Keywords: PhD, Studentship, Doctorate, Research Degree, mathematics; statistics; data analysis

More details in http://ueasciweb.uea.ac.uk/Resproject/show.aspx?ID=124