The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

Thesis (M.S.)--University of Delaware, 2009. / Principal faculty advisors: Kenneth E. Barner and Karl V. Steiner, Dept. of Electrical & Computer Engineering. Includes bibliographical references.

Thesis (Ph. D. in Applied Mathematics)--Naval Postgraduate School, June 2003. / Dissertation supervisors: Beny Neta, Dan Givoli. Includes bibliographical references (p. 131-133). Also available online.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

Thesis (Ph.D.)--George Mason University, 2009. / Vita: p. 108. Thesis co-directors: John Wallin, Thomas Wanner. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computational Science and Informatics. Title from PDF t.p. (viewed Oct. 12, 2009). Includes bibliographical references (p. 102-107). Also issued in print.

Thesis (Ph. D.)--California Institute of Technology, 2003. / "April 2004." Includes bibliographical references. EERL report series available at their website: http://caltecheerl.library.caltech.edu.

Thesis (M. Phil.)--University of Hong Kong, 1991.

Thesis (Ph. D.)--Washington State University, May 2009. / Title from PDF title page (viewed on June 3, 2009). "School of Electrical Engineering and Computer Science." Includes bibliographical references (p. 101-108).

Thesis (M.S.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaf 24). Also available on the World Wide Web.