My doctoral research dissertation focuses on two aspects of functional data analysis (FDA): FDA under spatial interdependence and FDA for multi-level data. The first part of my thesis focuses on developing modeling and inference procedure for functional data under spatial dependence. The methodology introduced in this part is motivated by a research study on inequities in accessibility to financial services. The first research problem in this part is concerned with a novel model-based method for clustering random time functions which are spatially interdependent. A cluster consists of time functions which are similar in shape. The time functions are decomposed into spatial global and time-dependent cluster effects using a semi-parametric model. We also assume that the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across curves from nearby locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small number of time points, high noise level and varying dependence structures. Over all simulation settings, the spatial-functional clustering method outperforms existing model-based clustering methods. In the case study presented in this project, we focus on estimates and classifies service accessibility patterns varying over a large geographic area (California and Georgia) and over a period of 15 years. The focus of this study is on financial services but it generally applies to any other service operation. The second research project of this part studies an association analysis of space-time varying processes, which is rigorous, computational feasible and implementable with standard software. We introduce general measures to model different aspects of the temporal and spatial association between processes varying in space and time. Using a nonparametric spatiotemporal model, we show that the proposed association estimators are asymptotically unbiased and consistent. We complement the point association estimates with simultaneous confidence bands to assess the uncertainty in the point estimates. In a simulation study, we evaluate the accuracy of the association estimates with respect to the sample size as well as the coverage of the confidence bands. In the case study in this project, we investigate the association between service accessibility and income level. The primary objective of this association analysis is to assess whether there are significant changes in the income-driven equity of financial service accessibility over time and to identify potential under-served markets. The second part of the thesis discusses novel statistical methodology for analyzing multilevel functional data including a clustering method based on a functional ANOVA model and a spatio-temporal model for functional data with a nested hierarchical structure. In this part, I introduce and compare a series of clustering approaches for multilevel functional data. For brevity, I present the clustering methods for two-level data: multiple samples of random functions, each sample corresponding to a case and each random function within a sample/case corresponding to a measurement type. A cluster consists of cases which have similar within-case means (level-1 clustering) or similar between-case means (level-2 clustering). Our primary focus is to evaluate a model-based clustering to more straightforward hard clustering methods. The clustering model is based on a multilevel functional principal component analysis. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small vs. moderate number of time points, high noise level and small number of measurement types. We demonstrate the applicability of the clustering analysis to a real data set consisting of time-varying sales for multiple products sold by a large retailer in the U.S. My ongoing research work in multilevel functional data analysis is developing a statistical model for estimating temporal and spatial associations of a series of time-varying variables with an intrinsic nested hierarchical structure. This work has a great potential in many real applications where the data are areal data collected from different data sources and over geographic regions of different spatial resolution.

Mit der vorliegenden Dissertation soll ein Beitrag zur Steigerung der Genauigkeit und Zuverlässigkeit einer sensorgestützten Objekterkennung im Fahrzeugumfeld geleistet werden. Aufbauend auf einem Erfassungssystem, bestehend aus einer Stereokamera und einem Mehrzeilen-Laserscanner, werden teils neu entwickelte Verfahren für die gesamte Verarbeitungskette vorgestellt. Zusätzlich wird ein neuartiges Framework zur Fusion heterogener Sensordaten eingeführt, welches über eine Zusammenführung der Fusionsergebnisse aus den unterschiedlichen Verarbeitungsebenen in der Lage ist, die Objektbestimmung zu verbessern. Nach einer Beschreibung des verwendeten Sensoraufbaus werden die entwickelten Verfahren zur Kalibrierung des Sensorpaares vorgestellt. Bei der Segmentierung der räumlichen Punktdaten werden bestehende Verfahren durch die Einbeziehung von Messgenauigkeit und Messspezifik des Sensors erweitert. In der anschließenden Objektverfolgung wird neben einem neuartigen berechnungsoptimierten Ansatz zur Objektassoziierung ein Modell zur adaptiven Referenzpunktbestimmung und –Verfolgung beschrieben. Durch das vorgestellte Fusions-Framework ist es möglich, die Sensordaten wahlweise auf drei unterschiedlichen Verarbeitungsebenen (Punkt-, Objekt- und Track-Ebene) zu vereinen. Hierzu wird ein sensorunabhängiger Ansatz zur Fusion der Punktdaten dargelegt, der im Vergleich zu den anderen Fusionsebenen und den Einzelsensoren die genaueste Objektbeschreibung liefert. Für die oberen Fusionsebenen wurden unter Ausnutzung der konkurrierenden Sensorinformationen neuartige Verfahren zur Bestimmung und Reduzierung der Detektions- und Verarbeitungsfehler entwickelt. Abschließend wird beschrieben, wie die fehlerreduzierenden Verfahren der oberen Fusionsebenen mit der optimalen Objektbeschreibung der unteren Fusionsebene für eine optimale Objektbestimmung zusammengeführt werden können. Die Effektivität der entwickelten Verfahren wurde durch Simulation oder in realen Messszenarien überprüft. / With the present thesis a contribution to the increase of the accuracy and reliability of a sensor-supported recognition and tracking of objects in a vehicle’s surroundings should be made. Based on a detection system, consisting of a stereo camera and a laser scanner, novel developed procedures are introduced for the whole processing chain of the sensor data. In addition, a new framework is introduced for the fusion of heterogeneous sensor data. By combining the data fusion results from the different processing levels the object detection can be improved. After a short description of the used sensor setup the developed procedures for the calibration and mutual orientation are introduced. With the segmentation of the spatial point data existing procedures are extended by the inclusion of measuring accuracy and specificity of the sensor. In the subsequent object tracking a new computation-optimized approach for the association of the related object hypotheses is presented. In addition, a model for a dynamic determination and tracking of an object reference point is described which exceeds the classical tracking of the object center in the track accuracy. By the introduced fusion framework it is possible to merge the sensor data at three different processing levels (point, object and track level). A sensor independent approach for the low fusion of point data is demonstrated which delivers the most precise object description in comparison to the other fusion levels and the single sensors. For the higher fusion levels new procedures were developed to discover and clean up the detection and processing mistakes benefiting from the competing sensor information. Finally it is described how the fusion results of the upper and lower levels can be brought together for an ideal object description. The effectiveness of the newly developed methods was checked either by simulation or in real measurement scenarios.

Introdução - A preocupação com a qualidade e disseminação dos dados em inquéritos é crescente no mundo. A integração entre banco de dados, planejamento da amostra, questionário e entrada de dados é fundamental para que resultados observados sejam válidos e precisos. A bibliografia pesquisada apontou que os inquéritos raramente produzem arquivos organizados, padronizados e prontos para disseminação, o que impossibilita estudar diferentes objetos de investigação com base em informações já coletadas. Objetivos - Implementar modelo hierárquico para entrada de dados em inquéritos epidemiológicos. Métodos - Foi utilizada a UML (Linguagem de Modelagem Unificada) para o projeto lógico e o Makeview do Epi Info para obtenção das estruturas de dados. Os testes foram feitos em um setor censitário do inquérito Acesso a Medicamentos - FAPESP. A documentação foi gerada no Makeview com ajuda de uma macro do Excel. Resultados - O modelo permite criar arquivos relacionais flexíveis, conforme a necessidade do objeto de estudo, com unidades estatísticas escolhidas dentre os 4 níveis hierárquicos: setor censitário, domicílios, indivíduos e questões específicas. Conclusão - A possibilidade de criar infinitas visões sobre os dados representa um avanço em comparação com o modelo plano. Deve ser usado como padrão em inquéritos epidemiológicos, pois permite estudar o efeito de conglomeração das unidades de análise, além de viabilizar a disseminação com dados organizados. O Epi Info pode ser usado para implementar modelos hierárquicos que considerem as variáveis do plano amostral. / Introduction - Concern about the quality and data dissemination in surveys is growing in the world. The integration between database, sample planning, questionnaire and data entry is fundamental to the accuracy and validity of the results. The bibliography showed that investigations rarely produce organized files, standardized and ready to dissemination, which makes impossible the study of various investigation objects based on information already collected. Goals - Implement hierarchical model for data entry in epidemiological surveys. Methods - It was used the UML (Unified Modeling Language) for the logical project and the Epi Info Makeview to obtain the data files. The tests were made in a census block of the Access to Medicines - FAPESP survey. The documentation was generated in Makeview with help of an Excel macro. Results - The model allows you to create flexible relational files, as the need to study subject, with statistical units chosen amongst the 4 hierarchical levels: census blocks, households, individuals and specific issues. Conclusion - The ability to create infinite views on the data represents a breakthrough in comparison to the flat files. It should be used as standard in epidemiological surveys, it allows studying the effect of conglomeration of analysis\' units, besides enabling the dissemination with organized data. The Epi Info can be used to implement hierarchical models that consider the variables of a sampling plan.

Introdução - A preocupação com a qualidade e disseminação dos dados em inquéritos é crescente no mundo. A integração entre banco de dados, planejamento da amostra, questionário e entrada de dados é fundamental para que resultados observados sejam válidos e precisos. A bibliografia pesquisada apontou que os inquéritos raramente produzem arquivos organizados, padronizados e prontos para disseminação, o que impossibilita estudar diferentes objetos de investigação com base em informações já coletadas. Objetivos - Implementar modelo hierárquico para entrada de dados em inquéritos epidemiológicos. Métodos - Foi utilizada a UML (Linguagem de Modelagem Unificada) para o projeto lógico e o Makeview do Epi Info para obtenção das estruturas de dados. Os testes foram feitos em um setor censitário do inquérito Acesso a Medicamentos - FAPESP. A documentação foi gerada no Makeview com ajuda de uma macro do Excel. Resultados - O modelo permite criar arquivos relacionais flexíveis, conforme a necessidade do objeto de estudo, com unidades estatísticas escolhidas dentre os 4 níveis hierárquicos: setor censitário, domicílios, indivíduos e questões específicas. Conclusão - A possibilidade de criar infinitas visões sobre os dados representa um avanço em comparação com o modelo plano. Deve ser usado como padrão em inquéritos epidemiológicos, pois permite estudar o efeito de conglomeração das unidades de análise, além de viabilizar a disseminação com dados organizados. O Epi Info pode ser usado para implementar modelos hierárquicos que considerem as variáveis do plano amostral. / Introduction - Concern about the quality and data dissemination in surveys is growing in the world. The integration between database, sample planning, questionnaire and data entry is fundamental to the accuracy and validity of the results. The bibliography showed that investigations rarely produce organized files, standardized and ready to dissemination, which makes impossible the study of various investigation objects based on information already collected. Goals - Implement hierarchical model for data entry in epidemiological surveys. Methods - It was used the UML (Unified Modeling Language) for the logical project and the Epi Info Makeview to obtain the data files. The tests were made in a census block of the Access to Medicines - FAPESP survey. The documentation was generated in Makeview with help of an Excel macro. Results - The model allows you to create flexible relational files, as the need to study subject, with statistical units chosen amongst the 4 hierarchical levels: census blocks, households, individuals and specific issues. Conclusion - The ability to create infinite views on the data represents a breakthrough in comparison to the flat files. It should be used as standard in epidemiological surveys, it allows studying the effect of conglomeration of analysis\' units, besides enabling the dissemination with organized data. The Epi Info can be used to implement hierarchical models that consider the variables of a sampling plan.