Estimation for state space models and Bayesian regression analysis with parameter constraints

Abstract

In the first part of this dissertation an estimation procedure for non-Gaussian state-space models is proposed. Typically, the likelihood function for non-Gaussian state-space models cannot be computed explicitly and so simulation based procedures, such as importance sampling or MCMC, are commonly used to estimate model parameters. In this dissertation, we consider an alternative estimation procedure which is based on an approximation to the likelihood function. The approximation can be computed and maximized directly, resulting in a quick estimation procedure without resorting to simulation. Moreover, this approach is competitive with estimates produced using simulation-based procedures. The speed of this procedure makes it viable to fit a wide range of potential models to the data and allows for bootstrapping the parameter estimates. In the second part of this dissertation an efficient Gibbs sampler for simulation of a multivariate normal random vector subject to inequality linear constraints is proposed. An application to a Bayesian linear model, where the regression parameters are subject to inequality linear constraints, is the primary motivation behind this research. Geweke (1991) and Robert (1995) have implemented the Gibbs sampler to the multivariate normal distribution subject to inequality linear constraints while the multiple linear regression with inequality constraints are considered for example by Chen and Deeley (1996) and Geweke (1996). However, these implementations can often exhibit poor mixing and slow convergence. The Gibbs sampler developed in this dissertation overcomes these limitations. In addition, it allows for the number of constraints to exceed the vector size and is able to cope with equality linear constraints.