Browsing by Author "William H. Swallow, Committee Member"

Now showing 1 - 2 of 2

Stepwise Hypothesis Testing with Applications in Pharmaceutical Responses
(2004-02-04) Gauvin, Jennifer Lynn Shannon; Dennis D. Boos, Committee Member; William H. Swallow, Committee Member; Roger L. Berger, Committee Chair; Anastasios Tsiatis, Committee Member
In some studies researchers seek to identify conditions under which a mean response exceeds a specified threshold. This work examines the case in which such conditions are defined in terms of two quantitative independent variables. For example, a pharmaceutical researcher might want to identify what values of dose and post-dose time yield an average blood concentration above a certain threshold. New methods of specifying a rectangular set of (time, dose) values for which the researcher can assert that the mean response exceeds the threshold are described. By using intersection-union tests applied in a stepwise fashion, the methods maintain a specified high probability that the rectangular set contains no (time, dose) values for which the mean response is lower than the threshold. The observations at each (time, dose) value must be independent, but neither method requires independent observations at different (time, dose) values. For example, concentrations measured on a subject at different time points may be correlated. Exact calculations and simulation studies are used to assess the error rates and performance properties of the new methods.
A Stochastic Volatility Model and Inference for the Term Structure of Interest
(2007-04-25) Liu, Peng; A. Ronald Gallant, Committee Member; Denis Pelletier, Committee Member; William H. Swallow, Committee Member; Peter Bloomfield, Committee Chair; David Dickey, Committee Member
This thesis builds a stochastic volatility model for the term structure of interest rates, which is also known as the dynamics of the yield curve. The main purpose of the model is to propose a parsimonious and plausible approach to capture some characteristics that conform to some empirical evidences and conventions. Eventually, the development reaches a class of multivariate stochastic volatility models, which is flexible, extensible, providing the existence of an inexpensive inference approach. The thesis points out some inconsistency among conventions and practice. First, yield curves and its related curves are conventionally smooth. But in the literature that these curves are modeled as random functions, the co-movement of points on the curve are usually assumed to be governed by some covariance structures that do not generate smooth random curves. Second, it is commonly agreed that the constant volatility is not a sound assumption, but stochastic volatilities have not been commonly considered in related studies. Regarding the above problems, we propose a multiplicative factor stochastic volatility model, which has a relatively simple structure. Though it is apparently simple, the inference is not, because of the presence of stochastic volatilities. We first study the sequential-Monte-Carlo-based maximum likelihood approach, which extends the perspectives of Gaussian linear state-space modeling. We propose a systematic procedure that guides the inference based on this approach. In addition, we also propose a saddlepoint approximation approach, which integrates out states. Then the state propagates by an exact Gaussian approximation. The approximation works reasonably well for univariate models. Moreover, it works even better for the multivariate model that we propose. Because we can enjoy the asymptotic property of the saddlepoint approximation.