Title: Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses
Abstract: The distributional transform and the continuous extension of a discrete random variable are amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Their 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 these methods. We investigate their small-sample and asymptotic efficiency for estimating high-dimensional multivariate normal copula models with univariate Bernoulli, Poisson, and negative binomial margins, and show that these approximations lead to biased estimates when there is more discretization. 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. The 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.