Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models

Authors:
Jerald F. Lawless;Yildiz E. Yilmaz
Affiliations:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada N2L 3G1;Samuel Lunenfeld Research Institute, Mount Sinai Hospital, Toronto, Ontario, Canada M5T 3L9
Venue:
Computational Statistics & Data Analysis
Year:
2011

Citing 4
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Abstract

We consider bivariate distributions that are specified in terms of a parametric copula function and nonparametric or semiparametric marginal distributions. The performance of two semiparametric estimation procedures based on censored data is discussed: maximum likelihood (ML) and two-stage pseudolikelihood (PML) estimation. The two-stage procedure involves less computation and it is of interest to see whether it is significantly less efficient than the full maximum likelihood approach. We also consider cases where the copula model is misspecified, in which case PML may be better. Extensive simulation studies demonstrate that in the absence of covariates, two-stage estimation is highly efficient and has significant robustness advantages for estimating marginal distributions. In some settings, involving covariates and a high degree of association between responses, ML is more efficient. For the estimation of association, PML does not offer an advantage.