On the classical estimation of bivariate copula-based Seemingly Unrelated Tobit models through the proposed inference function for augmented margins method

On the classical estimation of bivariate copula-based Seemingly Unrelated Tobit models through the proposed inference function for augmented margins method(*)

Abstract - This work performs the analysis of the bivariate Seemingly Unrelated (SUR) Tobit by modeling its nonlinear dependence structure through copula and assuming non-normal marginal error distributions. For model estimation, the use of copula methods enables the use of the (classical) Inference Function for Margins (IFM) method by Joe and Xu (1996), which is more computationally attractive (feasible) than the full maximum likelihood approach. However, our simulation study shows that the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in both margins. In order to obtain an unbiased estimate of the copula association parameter, we propose/develop a modified version of the IFM method, which we refer to as Inference Function for Augmented Margins (IFAM). Since the usual asymptotic approach, i.e. the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome, we propose the use of resampling procedures (bootstrap methods) to obtain confidence intervals for the copula-based SUR Tobit model parameters. The satisfactory results from the simulation and empirical studies indicate the adequate performance of our proposed model and methods. We illustrate our procedure using bivariate data on consumption of salad dressings and lettuce by U.S. individuals.

(*) Joint work with Francisco Louzada. 

Data: 15/04/2016 (sexta-feira), às 11 horas da manhã.

Local: Sala 13, no andar térreo do Instituto de Matemática da UFBA.

Apresentador: Paulo Henrique Ferreira da Silva

É Professor Adjunto da Universidade Federal da Bahia, junto ao Departamento de Estatística do Instituto de Matemática, e também Coordenador do Projeto CEP Online do Laboratório de Estudos do Risco (CER-USP). Possui graduação, mestrado e doutorado em Estatística pela Universidade Federal de São Carlos. Atua principalmente nas seguintes áreas: Regressão; Análise Multivariada; Análise de Sobrevivência e Confiabilidade; e Controle Estatístico de Processos.