Take our PhD survey
Take our PhD
survey for the
* or equivalent in Euros or US Dollars
21 May, 2013
Browse By Subject
Browse By Region
Professional Development (CPD)
PostDoc & PhD Jobs
PhD Research Project
This project is no longer listed in the FindAPhD database
and may not be available.
Click here to view other PhD studentship opportunities at University of East Anglia.
Copula modelling for non-normal multivariate data
University of East Anglia
School of Computing Sciences
Dr A Nikoloulopoulos
No more applications being accepted
Competition Funded PhD Project (Students Worldwide)
This research project is one of a number of projects at this institution. It is in competition for funding with one or more of these projects. Usually the project which receives the best applicant will be awarded the funding. Applications for this project are welcome from suitably qualified candidates worldwide. Funding may only be available to a limited set of nationalities and you should read the full department and project details for further information.
PhD Research Project
Multivariate response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences. Studying associations 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.) and/or limited dependence structure.
To solve this problem copulas seem to be a promising solution. Copulas are a currently popular and useful 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 flexible dependence modeling, different from assuming simple linear correlation structures and normality. Copulas, essentially, enable you to break the model building process into two separate steps:
(a) Choice of arbitrary marginal distributions:
(i) They could take different forms;
(ii) They could involve covariates.
(b) Choice of an arbitrary copula function (dependence structure).
That makes them particularly well suited to many applications in finance, insurance and medicine, among others.
This project will focus on dependence modeling with copulas for non-normal multivariate/longitudinal response data. Such data have different dependence structures including features such as tail dependence and/or negative dependence. To this end, the desiderata properties of multivariate copula families for modeling multivariate/longitudinal response data are given below (see e.g., Nikoloulopoulos and Karlis (2009) and Nikoloulopoulos et al. (2012)):
(a) Wide range of dependence, allowing both positive and negative dependence.
(b) Flexible dependence (including tail dependence for continuous data), meaning that the number of bivariate margins is (approximately) equal to the number of dependence parameters.
(c) Computationally feasible joint cumulative distribution function (discrete data) or density (continuous data) for likelihood estimation.
(d) Closure property under marginalization, meaning that lower-order margins belong to the same parametric family.
(e) No joint constraints for the dependence parameters, meaning that the use of covariate functions for the dependence parameters is straightforward.
In the existing literature, none of the existing parametric families of multivariate copulas satisfy all these conditions; hence there are many challenges for copula-based models for multivariate/longitudinal response data.
This project will deal with development of,
(a) models with some desirable properties (e.g., Nikoloulopoulos and Karlis (2009); Joe et al. (2010); Nikoloulopoulos et al. (2009, 2012)),
(b) computationally intensive yet tractable estimation methods (e.g., Nikoloulopoulos et al. (2011)),
with applications in biostatistics, finance, psychometrics, insurance, etc.
This project is funded specifically for international students, and provides full tuition fees and an annual stipend of £13,726 for three years. UK/EU students are welcome to apply but must be able to secure their own source of funding.
(i) Joe, H., Li, H., and Nikoloulopoulos, A. K. (2010). Tail dependence functions and vine copulas. Journal of Multivariate Analysis, 101:252-270.
(ii) Nikoloulopoulos, A. K., Joe, H., and Chaganty, N. R. (2011). Weighted scores method for regression models with dependent data. Biostatistics, 12:653-665.
(iii) Nikoloulopoulos, A. K., Joe, H., and Li, H. (2009). Extreme value properties of multivariate t copulas. Extremes, 12:129-148.
(iv) Nikoloulopoulos, A. K., Joe, H., and Li, H. (2012). Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics & Data Analysis, 56:3659-3673.
(v) Nikoloulopoulos, A. K. and Karlis, D. (2009). Finite normal mixture copulas for multivariate discrete data modeling. Journal of Statistical Planning and Inference, 139:3878-3890.
Like This PhD?
Add To Shortlist
PhD Provider Info
Visit Provider Website
All PhDs in this Dept
Send to a Friend
Printer Friendly Page
View A Larger Map
Nano Data Storage: Nanofabrication of magnetic structures for data storage applications
University of Manchester
School of Computer Science
Modelling network interactions - Modelling adaptive learning behaviour in dynamic stochastic networks
University of Leeds
Institute for Transport Studies (ITS)
The analysis of large transcriptomic data sets using distributed computing
Royal Holloway, University of London
Dept of Computer Science
Time & Space Efficient String Algorithms & Data Structures with Applications to Computational Biology
University of Liverpool
Faculty of Science and Engineering
Postgraduate Study Fair
MANCHESTER, 20 NOVEMBER 2013
Postgraduate Study & MBA Fair
LONDON, 30 JANUARY 2014
Like FindAPhD for news, events & competitions
Follow us on Twitter
Find A PhD
All rights reserved
Search for PhDs
PhDs by Subject
PhDs by Institution
PhDs by Region
Info for Students
PhD Study Guide
PhDs in the UK
PhD Funding Guide
Postgraduate Advice Forum
Postgraduate Email Updates
Info for Advertisers
Advertise a PhD
Banner & Buttons
Advertisers T & Cs
PostDoc & PhD Jobs
The Science Registry Ltd
, Sellers Wheel, 151 Arundel Street, Sheffield, S1 2NU, United Kingdom. Tel +44 (0) 114 268 4940 Fax: +44 (0) 114 268 5766
Clicking here will add this PhD to your PhD shortlist.
Your PhD shortlist allows you to easily browse, email & save projects and programmes.
Enquiry by Telephone
click to proceed
Enquiry by Email
click to proceed
Apply Online NOW!
click to visit
Add to and from your shortlist
click to add/remove
Click here to view the items added to your shortlist.