Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

An Analysis of the Implementation and Perceived Effectiveness of the SchoolMAX Family Portal

ABSTRACT Title of Document: AN ANALYSIS OF THE IMPLEMENTATION AND PERCEIVED EFFECTIVENESS OF THE SCHOOLMAX FAMILY PORTAL Warren Wesley Watts, Doctor of Education, 2015 Directed By: Margaret J. McLaughlin, Ph.D. Department of Counseling, Higher Education and Special Education School districts have spent millions of dollars implementing student information systems that offer family portals with web-based access to parents and students. One of the main purposes of these systems is to improve school-to-home communication. Research has shown that when school-to-home communication is implemented effectively, parent involvement improves and student achievement increases (Epstein, 2001). The purpose of the study was to (a) understand why parents used or refrained from using the family portal and (b) determine what barriers to use might exist. To this end, this descriptive study identified the information parent users accessed in the SchoolMAX family portal, determined how frequently parents accessed the portal, and ascertained whether parents perceived an increase in communication with their children about academic matters after they began accessing the portal. Finally, the study sought to identify whether barriers existed that prevented parents from using the family portal. The inquiry employed three data sources to answer the aforementioned queries. These sources included (a) a survey sent electronically to 19,108 parents who registered online for the SchoolMAX family portal; (b) SchoolMAX portal usage data from the student information system for system usage between January 1, 2015 and June 30, 2015; and (c) a paper survey sent to 691 parents of students that had never used the SchoolMAX family portal in one elementary school, one middle school and one high school that were representative of other schools in the district. Survey results indicated that parents at all grade levels used the family portal. Usage data also confirmed that approximately 19% of the students had parents who monitored their progress through the family portal. Usage data also showed that parents were monitoring approximately 25% of students in secondary schools (6th – 12th grade) and 16% of students in elementary schools. Of the wide menu of resources available through the SchoolMAX family portal, parents used three areas most frequently: attendance, daily grades, and report cards. Approximately 70% of parents responded that their communication had improved with their children about academic matters since they started using the SchoolMAX family portal, and 90% of parents responded that the SchoolMAX family portal was an effective or somewhat effective tool. Parents also expressed interest in the addition of additional information to the SchoolMAX family portal. Specifically, the top three additions parents wanted to see included homework assignments, high stakes test scores, and graduation requirements. Parents also reported that 92% of them spoke to their children at least 2 to 3 times per week about academics. Due to the low response rate of the parent non-user survey, potential barriers to using the SchoolMAX family portal could not be addressed in this study. However, this issue may be a useful research topic in a future study. Keywords: school to home communication, student information systems, family portal, parent portal

RACIAL/ETHNIC VARIABILITY IN THE EFFECT OF RADIATION ON SECOND PRIMARY THYROID CANCER IN CHILDREN: ANALYSIS USING SURVEILLANCE EPIDEMIOLOGY AND END RESULTS DATA

Increases in pediatric thyroid cancer incidence could be partly due to previous clinical intervention. This retrospective cohort study used 1973-2012 data from the Surveillance Epidemiology and End Results program to assess the association between previous radiation therapy exposure in development of second primary thyroid cancer (SPTC) among 0-19-year-old children. Statistical analysis included the calculation of summary statistics and univariable and multivariable logistic regression analysis. Relative to no previous radiation therapy exposure, cases exposed to radiation had 2.46 times the odds of developing SPTC (95% CI: 1.39-4.34). After adjustment for sex and age at diagnosis, Hispanic children who received radiation therapy for a first primary malignancy had 3.51 times the odds of developing SPTC compared to Hispanic children who had not received radiation therapy, [AOR=3.51, 99% CI: 0.69-17.70, p=0.04]. These findings support the development of age-specific guidelines for the use of radiation based interventions among children with and without cancer.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.