abstract: When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses. / Dissertation/Thesis / Arizona Medicare Data on Rehospitalization / Philippine Data on Children's Morbidity / M.S. Statistics 2012

Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

In order to evaluate a methane gas productivity of methane hydrate reservoirs, it is necessary to develop a numeric simulator predicting gas production behavior. For precise assessment of long-term gas productivity, it is important to develop a mathematical model which describes mechanical behaviors of methane hydrate reservoirs in consideration of their time-dependent properties and to introduce it into the numeric simulator. In this study, based on previous experimental results of triaxial compression tests of Toyoura sand containing synthetic methane hydrate, stress-strain relationships were formulated by variable-compliance-type constitutive model. The suggested model takes into account the time-dependent property obtained from laboratory investigation that time dependency of methane hydrate bearing sediment is influenced by methane hydrate saturation and effective confining pressure. Validity of the suggested model should be verified by other laboratory experiments on time-dependent behaviors of methane hydrate bearing sediment.

Simplifications regarding calculations of fatigue life due to vibrational loading is based on weakly stationarity assumptions which is a time independent method. The hypothesis was based on the uncertainty of these assumptions. The aim of this study was to examine whether the analysed data fulfilled the assumptions of weakly stationarity. It was determined that the assumption was not valid for most signals and a comparison of time dependent methods should be performed to evaluate the difference compared with the time independent method. Two time dependent methods were constructed and implemented on the signals based on the results of performed stationarity tests. The result determined that a decrease in fatigue life of an investigated weld might occur for the two time dependent methods compared with the time independent method. The method which was considered to produce the most accurate results was also the most constrained as to the amount of data that fulfilled its requirements. A conclusion was drawn that signals containing more data was necessary to achieve conclusive results of the fatigue life. The hypothesis was proven to be mostly true since most of the analysed signals were found to be piecewise weakly stationary.

This masters thesis is focused around the comparison of time dependent video grayscale conversion methods based on a user experiment. The test methodology is based on the pairwise comparison method 2AFC. It is composed of two test variants: a test with a reference video and a test without a reference video. The coefficients of agreement, consistency and correlation are utilized in the result analysis. The testing was done on 60 subjects which have done 7200 pairwise comparisons. The test results show that the time dependent method Hu14 is the most universal. Time dependent method Kim09 was bested by some non-dependent methods. The results also indicate that there is some correlation between the two test variants and that the choice of the input video can have impact on the method performance. The main contribution of this thesis is that non-dependent methods can under certain circumstances rival the performance of dependent methods and that the addition of a reference video did not have a meaningful impact on the test subjects judgements.