Finite mixture models
3938KbAbstractInitially, this thesis introduces a new graphical tool, that can be used replica hermes sz large womens belt
to summarise data possessing a mixture structure. Computation of the required summary statistics makes use of posterior probabilities of class membership obtained from a fitted mixture model. In this context, both real and simulated data are used to highlight the usefulness of the tool for the visualisation of mixture data in comparison to the use of a traditional boxplot. This thesis uses localised mixture models to produce predictions from time series data. Estimation method used in these models is achieved using a kernel weighted version of an EM algorithm: exponential kernels with different bandwidths are used as weight functions. By modelling a mixture of local regressions at a target time point, but using different bandwidths, an informative estimated mixture probabilities can be gained relating to the amount of information available in the data set. This information is given a scale of resolution, that corresponds to each bandwidth. Nadaraya Watson and local linear estimators are used to carry out localised estimation. For prediction at a future time point, a new methodology of bandwidth selection and adequate methods are proposed for each local method, and then compared to competing forecasting routines. A simulation study is executed to assess the performance of this model for prediction. Finally, double localised mixture models are presented, that can be used to improve predictions for a variable time series using additional information provided by other time series. Estimation for these models is achieved using a double kernel weighted version of the EM algorithm, employing exponential kernels with different horizontal bandwidths and normal kernels with different vertical bandwidths, that are focused around a target observation at a given time point. Nadaraya Watson and local linear estimators are used to carry out the double localised estimation. For prediction at a future time point, different approaches are considered for each local method, and are compared to competing forecasting routines. Real data is used to investigate the performance of the localised and double localised mixture models for prediction. The data used predominately in this thesis is taken from the International Energy Agency (IEA).