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Title: Joint modeling of mean and scale covariance using empirical likelihood Authors:  Senay Ozdemir - Afyon Kocatepe University (Turkey) [presenting]
Yesim Guney - Ankara University (Turkey)
Olcay Arslan - Ankara University (Turkey)
Abstract: A joint mean and covariance model enables the determination of the mean and covariance structure, which has an important role in longitudinal studies that can be used for observation units that are re-measured over time. Some difficulties, including failure to achieve positive definiteness, are encountered in the estimation of the covariance structure in this model. To overcome these difficulties in obtaining the covariance matrix, the modified Cholesky decomposition can be used. The model parameters are widely estimated with the maximum likelihood estimation method, which requires a distribution assumption on error terms. Instead of making the distribution assumption, which causes some difficulties in practice, the usability of the empirical likelihood method, which offers a more flexible estimation by using the information in the sample, can be considered. The empirical likelihood method performs as maximizing empirical likelihood function consisting of probabilistic weights assigned to observations, under some constraints, which includes the weighted forms of estimating equations obtained from maximum likelihood. A small simulation study will be provided to assess the performance of the proposed estimator.