Abstract
The distributional transform (DT) is amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Its advantage is that the likelihood can be derived
conveniently under the theory for copula models with continuous margins, but there has not been a clear analysis of the adequacy of this method. We investigate the small-sample and asymptotic efficiency of the method for estimating high-dimensional multivariate normal copula models with univariate
Bernoulli, Poisson, and negative binomial margins, and show that the DT approximation leads to biased estimates when there is more discretisation. For a high-dimensional discrete response, we implement a maximum simulated likelihood method, which is based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods. Efficiency calculations show that our method is nearly as efficient as maximum likelihood for fully specified high-dimensional multivariate normal copula models. Both
methods are illustrated with spatially aggregated count data sets, and it is shown that there is a substantial gain on efficiency via the maximum simulated likelihood method.
conveniently under the theory for copula models with continuous margins, but there has not been a clear analysis of the adequacy of this method. We investigate the small-sample and asymptotic efficiency of the method for estimating high-dimensional multivariate normal copula models with univariate
Bernoulli, Poisson, and negative binomial margins, and show that the DT approximation leads to biased estimates when there is more discretisation. For a high-dimensional discrete response, we implement a maximum simulated likelihood method, which is based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods. Efficiency calculations show that our method is nearly as efficient as maximum likelihood for fully specified high-dimensional multivariate normal copula models. Both
methods are illustrated with spatially aggregated count data sets, and it is shown that there is a substantial gain on efficiency via the maximum simulated likelihood method.
Original language | English |
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Pages (from-to) | 493-505 |
Journal | Stochastic Environmental Research and Risk Assessment |
Volume | 30 |
Issue number | 2 |
Early online date | 21 Mar 2015 |
DOIs | |
Publication status | Published - Feb 2016 |
Keywords
- Areal data
- Distributional transform
- Generalized quantile transform
- Rectangle probabilities
- Simulated likelihood
- Spatially aggregated data
Profiles
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Aristidis K. Nikoloulopoulos
- School of Engineering, Mathematics and Physics - Associate Professor in Statistics
- Numerical Simulation, Statistics & Data Science - Member
Person: Research Group Member, Academic, Teaching & Research