Mixed-Effects State Space Models With Disturbances Of GED

Many studies have been done on state space models after its proposed, in most of whicherror disturbance are assumed to be of normal distributions. But real data are sometimes notof, for example, real stock data and species' data in biology. We present a modified modelbased on mixed-effects state space model, mixed-effects state space model with general errordistribution.In the section of introductions, we introduce the past study on state space models insimple, points out the wanting of study on data of heavy tails.Chapter 1, we first introduce the basic expression of mixed-effects state space model.Establish the mixed-effects state space model with general error distribution, based on the oldone. We then simplify the new model to our extent, and points out that, the new one is ageneralization to the old one.Chapter 2, we discuss the parameters' estimation with Bayesian method. First give outthe full conditional distributions of every parameter of model. After introducing the simplerejection sampling, and the adaptive rejection sampling method for density functions ofog-concave, we present new adaptive rejection sampling methods for density functions oflog-convex and log-concave-plus-convex, sampling methods for compound Gamma densityfunctions, and also, approximate sampling for index variable of general error distributioninvolved in our new model. With the methods introduced, we discuss the detailed samplingwork of parameter estimation with Bayesian approach.Chapter 3, we first present a simulation on parameter estimation of our new model,indicating its utility on data of heavy tails. Employ new model on real stock data forparameter estimation and forecasting, and compare the results with that of mixed-effects statespace model to show the priority to the old one. And at last, employ new model on HIV datafor indicating its advantage on eliminating the effects caused by awful selection on indexparameter of general error distribution.In the section of conclusion, we summarize the results and discuss the possibleextensions to our models and study.