PhD opportunity at UEA: HIGH-DIMENSIONAL COPULA REGRESSION

Dear GRstats,

I am pleased to announce a PhD opportunity at the University of East Anglia that is open for applications. The PhD project is entitled “High-dimensional copula regression”.

Further details are outlined below.

Best wishes,

Aris

Dr Aristidis K. Nikoloulopoulos | Associate Professor in Statistics |  School of Computing Sciences
University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ
E-mail: a.nikoloulopoulos@uea.ac.uk  | Web: https://people.uea.ac.uk/a_nikoloulopoulos

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APPLICATION DEADLINE

15th January 2021

LOCATION

University of East Anglia

START DATE

1st October 2021

SUPERVISOR

Dr Aristidis K. Nikoloulopoulos https://people.uea.ac.uk/a_nikoloulopoulos

PROJECT OVERVIEW

Multivariate discrete response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences. For multivariate discrete data given a vector of (continuous or discrete) covariates, the discretized multivariate (MVN) distribution, or the MVN copula with discrete margins, has been in use for a considerable length of time, and much earlier in the biostatistics, psychometrics, and econometrics literature. It is usually known as a multivariate, or multinomial, probit model. The multivariate probit model is a simple example of the MVN copula with univariate probit regressions as the marginals.

The MVN copula generated by the MVN distribution inherits the useful properties of the latter, thus allowing a wide range for dependence, and overcomes the drawback of limited dependence inherent in simple parametric families of copulas. The use of the MVN with logistic regression (or Poisson or negative binomial regression) is just a special case of the general theory of dependence modelling with copulas. Implementation of the MVN copula for discrete data (discretized MVN) is possible, but not easy, because the MVN distribution as a latent model for discrete response requires rectangle probabilities based on high-dimensional integrations or their approximations.

The project will target multidimensional regression models for high-dimensional discrete response data. A unified and efficient framework of such regression models will be established with the utility of the MVN copula or discretized MVN. The aim is to utilise advanced inferential methods, to estimate the model parameters when the interest is to the univariate or dependence parameters. The interest will be to efficiently estimate both the marginal and dependence parameters; that is the dependence will not be treated as nuisance, i.e., it will be assumed that joint and conditional probabilities are of interest.


REFERENCES

Nikoloulopoulos, A. K. (2013). 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.

Nikoloulopoulos, A. K. (2016). Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environmental Research and Risk Assessment, 30(2):493–505.

Nikoloulopoulos, A. K. (2016). Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria. Statistics in Medicine, 35:2377–2390.

Nikoloulopoulos, A.K. (2020) Weighted scores estimating equations and CL1 information criteria for longitudinal ordinal response. Journal of Statistical Computation and Simulation, 90: 2002–2022.

Nikoloulopoulos, A. K., Joe, H., and Chaganty, N. R. (2011). Weighted scores method for regression models with dependent data. Biostatistics, 12:653–665.


ENTRY REQUIREMENTS

This project requires a 1st. Acceptable 1st degrees are Mathematics, Statistics, or Actuarial Science.

FUNDING

This PhD project is in a competition for a 3 year UEA funded studentship covering stipend (£15,285 pa), tuition fees (Home only) and research costs. International applicants (EU/non-EU) are eligible for UEA funded studentships but they are required to fund the difference between Home and International tuition fees.

APPLICATION PROCESS

Full details and the application process can be found at https://www.uea.ac.uk/course/phd-doctorate/high-dimensional-copula-regression-nikoloulopoulosa-u21scio. For more information on the project, please contact Dr Aristidis K. Nikoloulopoulos a.nikoloulopoulos@uea.ac.uk