No description available.

This thesis advocates the use of maximum likelihood analysis for generalized regression models with measurement error in a single explanatory variable. This will be done first by presenting a computational algorithm and the numerical details for carrying out this algorithm on a wide variety of models. The computational methods will be based on the EM algorithm in conjunction with the use of Gauss-Hermite quadrature to approximate integrals in the E-step. Second, this thesis will demonstrate the relative superiority of likelihood-ratio tests and confidence intervals over those based on asymptotic normality of estimates and standard errors, and that likelihood methods may be more robust in these situations than previously thought. The ability to carry out likelihood analysis under a wide range of distributional assumptions, along with the advantages of likelihood ratio inference and the encouraging robustness results make likelihood analysis a practical option worth considering in regression problems with explanatory variable measurement error. / Graduation date: 1999

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Wenbo Li, Dept. of Mathematical Sciences. Includes bibliographical references.

by Sze Tsz-leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 91). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Basic concepts of Monte Carlo integration --- p.1 / Chapter 1.1.1 --- Importance sampling --- p.4 / Chapter 1.1.2 --- Control variate --- p.5 / Chapter 1.1.3 --- Antithetic variate --- p.6 / Chapter 1.1.4 --- Stratified sampling --- p.7 / Chapter 1.1.5 --- Biased Estimator --- p.10 / Chapter 1.2 --- Some special methods in Monte Carlo integration --- p.11 / Chapter 1.2.1 --- Haber´ةs modified Monte Carlo quadrature I --- p.11 / Chapter 1.2.2 --- Haber's modified Monte Carlo quadrature II --- p.11 / Chapter 1.2.3 --- Weighted Monte Carlo integration --- p.12 / Chapter 1.2.4 --- Adaptive importance sampling --- p.13 / Chapter Chapter 2 --- New methods / Chapter 2.1 --- The use of Newton Cotes quadrature formulae in stage one --- p.17 / Chapter 2.1.1 --- Using one-dimensional trapezoidal rule --- p.17 / Chapter 2.1.2 --- Using two-dimensional or higher dimensional product trapezoidal rule --- p.21 / Chapter 2.1.3 --- Extension to higher order one-dimensional Newton Cotes formulae --- p.32 / Chapter 2.2 --- The use of Guass quadrature rule in stage one --- p.45 / Chapter 2.3 --- Some variations of the new methods --- p.56 / Chapter 2.3.1 --- Using probability points in both stages --- p.56 / Chapter 2.3.2 --- Importance sampling --- p.59 / Chapter 2.3.2.1 --- Triangular distribution --- p.60 / Chapter 2.3.2.2 --- Beta distribution --- p.64 / Chapter Chapter 3 --- Examples / Chapter 3.1 --- Example one: using trapezoidal rule as basic rule --- p.73 / Chapter 3.1.1 --- One-dimensional case --- p.73 / Chapter 3.1.2 --- Two-dimensional case --- p.80 / Chapter 3.2 --- Example two: Using Simpson's 3/8 rule as basic rule --- p.85 / Chapter 3.3 --- Example three： Using Guass rule as basic rule --- p.86 / Chapter Chapter 4 --- Conclusion and discussions --- p.88 / Reference --- p.91

This thesis considers likelihood inferences for generalized linear models with additional random effects. The likelihood function involved ordinarily cannot be evaluated in closed form and numerical integration is needed. The theme of the thesis is a closed-form approximation based on Laplace's method. We first consider a special yet important case of the above general setting -- the Mantel-Haenszel-type model with overdispersion. It is seen that the Laplace approximation is very accurate for likelihood inferences in that setting. The approach and results on accuracy apply directly to the more general setting involving multiple parameters and covariates. Attention is then given to how to maximize out nuisance parameters to obtain the profile likelihood function for parameters of interest. In evaluating the accuracy of the Laplace approximation, we utilized Gauss-Hermite quadrature. Although this is commonly used, it was found that in practice inadequate thought has been given to the implementation. A systematic method is proposed for transforming the variable of integration to ensure that the Gauss-Hermite quadrature is effective. We found that under this approach the Laplace approximation is a special case of the Gauss-Hermite quadrature. / Graduation date: 1994

This dissertation presents a self-tuning regulator (STR) design method developed based upon a state-space linear quadratic Gaussian (LQG) control strategy for rejecting a disturbance in a flexible structure in the face of model uncertainty. The parameters to be tuned are treated as additional state variables and are estimated recursively together with the system state that is needed for feedback. Also, the feedback gains are designed in the LQ framework based upon the estimated model parameters. Two problems concerning the uncertainty of model parameters are recognized. First, we consider the uncertainty in the system matrix of the state space model. The self-tuning regulator is implemented by computer and the control law is obtained based upon a discrete-time model; however, only selected continuous-time parameters with physical meanings to which the controller is highly sensitive are tuned. It is formulated as a nonlinear filtering problem such that both the estimated state and the unknown parameters can be obtained by an extended Kahman filter. The capability of this design method is experimentally demonstrated by applying it to the rejection of a disturbance in a simply supported plate. The other problem considered is that the location where the disturbance enters the system is unknown. This corresponds to an unknown disturbance influence matrix. Under the assumption that the system matrix is known and the disturbance can be measured, it is formulated as a linear filtering problem with an approximate discrete-time design model. Similarly, the estimated state for feedback and the unknown parameters are identified simultaneously and recursively. Also, the feedback gains are calculated approximately by recursively solving the discrete-time control Riccati equation. The effectiveness of the controller is shown by applying it to a simply-supported plate, when the location of the disturbance is assumed unknown. Since implementing LQG self-tuning controllers for vibration control systems requires significant real-time computation, methods that can reduce the computing load are examined. In addition, the possibility of extending the self tuning to disturbance model parameters is explored. / Ph. D.

Indiana University-Purdue University Indianapolis (IUPUI) / Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects, as well as their functional forms is essential for practical data analysis. However, no existing methods have been developed to meet this need in a joint model setting. In this dissertation, I describe a penalized likelihood-based method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for model selection. By reparameterizing variance components through a Cholesky decomposition, I introduce a penalty function of group shrinkage; the penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. The functional forms of the independent effects are determined through a procedure for structural discovery. Specifically, I first construct the model by penalized cubic B-spline and then decompose the B-spline to linear and nonlinear elements by spectral decomposition. The decomposition represents the model in a mixed-effects model format, and I then use the mixed-effects variable selection method to perform structural discovery. Simulation studies show excellent performance. A clinical application is described to illustrate the use of the proposed methods, and the analytical results demonstrate the usefulness of the methods.