| Summary: | In multivariate regression, researchers are interested in modeling a correlated
multivariate response variable as a function of covariates. The response of
interest can be multidimensional; the correlation between the elements of
the multivariate response can be very complex. In many applications, the
association between the elements of the multivariate response is typically
treated as a nuisance parameter. The focus is on estimating efficiently the
regression coefficients, in order to study the average change in the mean
response as a function of predictors. However, in many cases, the estimation of the covariance and, where applicable, the temporal dynamics of the
multidimensional response is the main interest, such as the case in finance,
for example. Moreover, the correct specification of the covariance matrix is
important for the efficient estimation of the regression coefficients. These
complex models usually involve some parameters that are static and some
dynamic. Until recently, the simultaneous estimation of dynamic and static
parameters in the same model has been difficult. The introduction of particle MCMC algorithms by Andrieu and Doucet (2002) has allowed for the possibility of considering such models. In this thesis, we propose a general
framework for jointly estimating the covariance matrix of multivariate data
as well as the regression coefficients. This is done under different settings,
for different dimensions and measurement scales. === Science, Faculty of === Statistics, Department of === Graduate
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