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Title: Joint modeling of mean and dispersion of the multivariate Laplace distribution Authors:  Olcay Arslan - Ankara University (Turkey) [presenting]
Yesim Guney - Ankara University (Turkey)
Fulya Gokalp Yavuz - Middle East Technical University (Turkey)
Abstract: An alternative robust approach is proposed to joint modeling of mean and scale covariance using multivariate Laplace distribution. The multivariate Laplace distribution has the same number of parameters as the multivariate normal distribution, but similar to the multivariate t-distribution. It is a heavy-tailed alternative distribution to the multivariate normal distribution. Since it has fewer parameters, the estimation procedure will be less complicated compared to the t-distribution. After we set the model, a modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. The parameter estimation is carried on using the maximum likelihood estimation method. The technique for the prediction of future responses is also investigated. The Fisher scoring algorithm and the EM algorithm are provided to compute the estimates. An extensive simulation study and a real data example are provided to demonstrate the performance of the proposed method based on Laplace distribution for jointly modeling mean and covariance.