Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses

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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.
Original languageEnglish
Pages (from-to)493-505
JournalStochastic Environmental Research and Risk Assessment
Volume30
Issue number2
Early online date21 Mar 2015
DOIs
Publication statusPublished - Feb 2016

Keywords

  • Areal data
  • Distributional transform
  • Generalized quantile transform
  • Rectangle probabilities
  • Simulated likelihood
  • Spatially aggregated data

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