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Estimation for State-Space Models and Bayesian
Regression Analysis with Parameter Constraints
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Gabriel
Rodriguez-Yam, Statistics Department, Colorado State University
Monday, 03 November 2003
1:10 PM
B4 Engineering Building
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 can not be computed explicitly and so
simulation based procedures, such as importance sampling or MCMC, are
commonly used to estimate model parameters. In this paper, 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
Geweke (1996) and Chen and Deely (1996). However, these implementations can
often exhibit poor mixing and slow convergence. This paper overcomes these
limitations and, in addition, allows for the number of constraints to
exceed the vector size and is able to cope with equality linear
constraints.
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