Empirical likelihood based longitudinal studies

In longitudinal data analysis, our primary interest is in the regression parameters for the marginal expectations of the longitudinal responses; the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly for correlated discrete outcome data. Marginal modeling approaches such as generalized estimating equations (GEEs) have received much attention in the context of longitudinal regression. These methods are based on the estimates of the first two moments of the data and the working correlation structure. The confidence regions and hypothesis tests are based on the asymptotic normality. The methods are sensitive to misspecification of the variance function and the working correlation structure. Because of such misspecifications, the estimates can be inefficient and inconsistent, and inference may give incorrect results. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its characteristics and asymptotic properties. We also provide an algorithm based on EL principles for the estimation of the regression parameters and the construction of a confidence region for the parameter of interest. We extend our approach to variable selection for highdimensional longitudinal data with many covariates. In this situation it is necessary to identify a submodel that adequately represents the data. Including redundant variables may impact the model’s accuracy and efficiency for inference. We propose a penalized empirical likelihood (PEL) variable selection based on GEEs; the variable selection and the estimation of the coefficients are carried out simultaneously. We discuss its characteristics and asymptotic properties, and present an algorithm for optimizing PEL. Simulation studies show that when the model assumptions are correct, our method performs as well as existing methods, and when the model is misspecified, it has clear advantages. We have applied the method to two case examples.

Regional flood frequency analysis for Newfoundland and Labrador using the L-Moments index-flood method

The L-moments based index-flood procedure had been successfully applied for Regional Flood Frequency Analysis (RFFA) for the Island of Newfoundland in 2002 using data up to 1998. This thesis, however, considered both Labrador and the Island of Newfoundland using the L-Moments index-flood method with flood data up to 2013. For Labrador, the homogeneity test showed that Labrador can be treated as a single homogeneous region and the generalized extreme value (GEV) was found to be more robust than any other frequency distributions. The drainage area (DA) is the only significant variable for estimating the index-flood at ungauged sites in Labrador. In previous studies, the Island of Newfoundland has been considered as four homogeneous regions (A,B,C and D) as well as two Water Survey of Canada's Y and Z sub-regions. Homogeneous regions based on Y and Z was found to provide more accurate quantile estimates than those based on four homogeneous regions. Goodness-of-fit test results showed that the generalized extreme value (GEV) distribution is most suitable for the sub-regions; however, the three-parameter lognormal (LN3) gave a better performance in terms of robustness. The best fitting regional frequency distribution from 2002 has now been updated with the latest flood data, but quantile estimates with the new data were not very different from the previous study. Overall, in terms of quantile estimation, in both Labrador and the Island of Newfoundland, the index-flood procedure based on L-moments is highly recommended as it provided consistent and more accurate result than other techniques such as the regression on quantile technique that is currently used by the government.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.