van Norden and Schaller (1996) develop a standard regime-switching model to study stock market crashes. In their seminal paper, they use the maximum likelihood estimation to estimate the model parameters and show that a two-regime speculative bubble model has significant explanatory power for stock market returns in some observed periods. However, it is well known that the maximum likelihood estimation can lead to bias if the model contains multiple local maximum points or the estimation starts with poor initial values. Therefore, a better approach to estimate the parameters in the regime-switching models is to be found. One possible way is the Bayesian Gibbs-sampling approach, where its advantages are well discussed in Albert and Chib (1993). In this thesis, the Bayesian Gibbs-sampling estimation is examined by using two U.S. stock datasets: CRSP monthly value-weighted index from Jan 1926 to Dec 2010 and S&P 500 index from Jan 1871 to Dec 2010. It is found that the Gibbs-sampling estimation explains the U.S. data better than the maximum likelihood estimation. Moreover, the existing standard regime-switching speculative behaviour model is extended by considering the time-varying transition probabilities which are governed by the first-order Markov chain. It is shown that the time-varying first-order transition probabilities of Markov regime-switching speculative rational bubbles can lead stock market returns to have a second-order Markov regime. In addition, a Bayesian Gibbs-sampling algorithm is developed to estimate the parameters in the second-order two-state Markov regime-switching model. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Computer adaptive testing (CAT) has grown both in research and implementation. Test construction and security issues, however, have led many to reconsider the merits of CAT. Multistage testing (MST) is an alternative adaptive test design that purportedly addresses CAT's shortcomings. Yet considerably less research has been conducted on MST. Also, most research in adaptive testing has been based on item response theory (IRT). Many tests now make use of testlets -- bundles of items administered together, often based on a common stimulus. The use of testlets violates local independence, a fundamental assumptions of IRT. Testlet response theory (TRT) is a relatively new measurement model designed to measure testlet-based tests. Few studies though have examined its use in testlet-based CAT and MST designs. This dissertation investigated the performance of testlet-based CATs and MSTs measured using the TRT model. The test designs compared included a CAT that is adaptive at the testlet level only (testlet-level CAT), a CAT that is adaptive at both the testlet and item levels (item-level CAT) and a MST design (MST). Test conditions manipulated included test length, item pool size, and examinee ability distribution. Examinee data were generated using TRT-calibrated item parameters based on data from a large-scale reading assessment. The three test designs were evaluated based on measurement effectiveness and exposure control properties. The study found that all three adaptive test designs yielded similar and good measurement accuracy. Overall, the item-level CAT produced better measurement precision, followed by the MST design. However, the MST and CAT designs yielded better measurement precision at different areas of the ability scale. All three test designs yielded acceptable exposure control properties at the testlet level. At the item level, the testlet-level CAT produced the best overall result. The item-level CAT had less than ideal pool utilization, but was able to meet its pre-specified maximum exposure control rate and maintain low item exposure rates. The MST had excellent pool utilization, but a higher percentage of items with high exposure rates. Skewing the underlying ability distribution also had a particularly notable negative effect on the exposure control properties of the MST. / text

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published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

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