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

Nikoloulopoulos, Aristidis K ORCID: https://orcid.org/0000-0003-0853-0084 (2016) Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environmental Research and Risk Assessment, 30 (2). pp. 493-505. ISSN 1436-3240

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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.

Item Type:	Article
Uncontrolled Keywords:	areal data,distributional transform,generalized quantile transform,rectangle probabilities,simulated likelihood,spatially aggregated data
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Statistics (former - to 2024) Faculty of Science > Research Groups > Numerical Simulation, Statistics & Data Science
Related URLs:	http://arxiv.org/abs/1411.1869
Depositing User:	Pure Connector
Date Deposited:	23 Mar 2015 11:00
Last Modified:	08 Nov 2024 09:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/52829
DOI:	10.1007/s00477-015-1060-2

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