A disseminação de sistemas de aquisição de dados sobre a qualidade e o desempenho de produtos e processos de fabricação deu origem a novos tipos de dados. Dado funcional é um conjunto de dados que formam um perfil ou uma curva. No perfil, a característica de qualidade é uma função dependente de uma ou mais variáveis exploratórias ou independentes. A análise de dados funcionais é um tema de pesquisa recente praticado em diversas áreas do conhecimento. Na indústria, os dados funcionais aparecem no controle de qualidade. A ausência de métodos apropriados a dados funcionais pode levar ao uso de métodos ineficientes e reduzir o desempenho e a qualidade de um produto ou processo. A análise de dados funcionais através de métodos multivariados pode ser inadequada devido à alta dimensionalidade e estruturas de variância e covariância dos dados. O desenvolvimento teórico de métodos para a análise de dados funcionais na área de Engenharia da Qualidade encontra-se defasado em relação ao potencial de aplicações práticas. Este trabalho identificou a existência dos dados funcionais tratados por métodos ineficientes. Os métodos atuais para controle de qualidade de dados são adaptados a situações específicas, conforme o tipo de dado funcional e a fase do monitoramento. Este trabalho apresenta propostas para métodos de análise de dados funcionais aplicáveis a questões relevantes da área de pesquisa em Engenharia da Qualidade, tais como: (i) o uso da análise de variância em experimentos com dados funcionais; (ii) gráficos de controle para monitoramento de perfis; e (iii) a análise e seleção de perfis de fornecedores em projetos inovadores. / The dissemination of data acquisition systems on the quality and performance of products and manufacturing process has given rise to new types of data. Functional data are a collection of data points organized as a profile or curve. In profile, the quality characteristic is a function dependent on one or more exploratory or independent variables. The functional data analysis is a recent research topic practiced in various areas of knowledge. In industry, the functional data appears in quality control. The lack of suitable methods can lead to use of inefficient methods and reducing the performance and quality of a product or process. The analysis of functional data by multivariate methods may be inadequate due to the high dimensionality and variance and covariance structures of the data. The development of theoretical methods for the analysis of functional data in Quality Engineering area is lagged behind the potential for practical applications. This work identified the existence of functional data processed by inefficient methods. Current methods for data quality control are adapted to specific situations, depending on the type of functional data and the phase of monitoring. This paper presents proposals for functional data analysis methods applicable to relevant research questions in the area of Quality Engineering such as: (i) the use of analysis of variance in experiments with functional data; (ii) control charts for monitoring profiles; and (iii) the analysis and selection of supplier profiles on innovative projects.

A disseminação de sistemas de aquisição de dados sobre a qualidade e o desempenho de produtos e processos de fabricação deu origem a novos tipos de dados. Dado funcional é um conjunto de dados que formam um perfil ou uma curva. No perfil, a característica de qualidade é uma função dependente de uma ou mais variáveis exploratórias ou independentes. A análise de dados funcionais é um tema de pesquisa recente praticado em diversas áreas do conhecimento. Na indústria, os dados funcionais aparecem no controle de qualidade. A ausência de métodos apropriados a dados funcionais pode levar ao uso de métodos ineficientes e reduzir o desempenho e a qualidade de um produto ou processo. A análise de dados funcionais através de métodos multivariados pode ser inadequada devido à alta dimensionalidade e estruturas de variância e covariância dos dados. O desenvolvimento teórico de métodos para a análise de dados funcionais na área de Engenharia da Qualidade encontra-se defasado em relação ao potencial de aplicações práticas. Este trabalho identificou a existência dos dados funcionais tratados por métodos ineficientes. Os métodos atuais para controle de qualidade de dados são adaptados a situações específicas, conforme o tipo de dado funcional e a fase do monitoramento. Este trabalho apresenta propostas para métodos de análise de dados funcionais aplicáveis a questões relevantes da área de pesquisa em Engenharia da Qualidade, tais como: (i) o uso da análise de variância em experimentos com dados funcionais; (ii) gráficos de controle para monitoramento de perfis; e (iii) a análise e seleção de perfis de fornecedores em projetos inovadores. / The dissemination of data acquisition systems on the quality and performance of products and manufacturing process has given rise to new types of data. Functional data are a collection of data points organized as a profile or curve. In profile, the quality characteristic is a function dependent on one or more exploratory or independent variables. The functional data analysis is a recent research topic practiced in various areas of knowledge. In industry, the functional data appears in quality control. The lack of suitable methods can lead to use of inefficient methods and reducing the performance and quality of a product or process. The analysis of functional data by multivariate methods may be inadequate due to the high dimensionality and variance and covariance structures of the data. The development of theoretical methods for the analysis of functional data in Quality Engineering area is lagged behind the potential for practical applications. This work identified the existence of functional data processed by inefficient methods. Current methods for data quality control are adapted to specific situations, depending on the type of functional data and the phase of monitoring. This paper presents proposals for functional data analysis methods applicable to relevant research questions in the area of Quality Engineering such as: (i) the use of analysis of variance in experiments with functional data; (ii) control charts for monitoring profiles; and (iii) the analysis and selection of supplier profiles on innovative projects.

Neste trabalho, estudam-se métodos que consideram a natureza funcional da Estrutura a Termo da Taxa de Juros (ETTJ) para fazer previsões fora da amostra. São estimados modelos não-paramétricos para dados funcionais (NP-FDA) e séries temporais funcionais (FTS). O primeiro se baseia em um estimador de regressão proposto por Ferraty e Vieu (2006), que utiliza funções Kernel para atribuir pesos localmente às variáveis funcionais. Já o segundo se baseia no trabalho de Hays, Shen e Huang (2012), que estimam a ETTJ através de um modelo de fatores dinâmicos, que por sua vez são estimados através de análise de componentes principais funcional. Testa-se a capacidade de previsão dos modelos com a ETTJ americana, para os horizontes de 1, 3, 6 e 12 meses, e comparam-se os resultados com modelos benchmark, como Diebold e Li (2006) e o passeio aleatório. Principal foco deste trabalho, as estimações com métodos NP-FDA não tiveram resultado muito bons, obtendo sucesso apenas com maturidades e horizontes muito curtos. Já as estimações com FTS tiveram, no geral, desempenho melhor que os métodos escolhidos como benchmark. / This work studies methods that takes the Yield Curve's functional nature into account to produce out-of-sample forecasts. These methods are based in nonparametric functional data analysis (NP-FDA) and functional time series (FTS). The former are based in a functional regressor estimator proposed by Ferraty e Vieu (2006) that includes Kernel functions to do local weighting between the functional variables. The latter are based on the paper by Hays, Shen and Huang (2012), that forecasts the Yield Curve based in a dynamic factors model, in which the factors are determined by functional principal component analysis. Their forecasting capability is tested for the american's Yield Curve database for 1, 3, 6 and 12 months. The results from the functional methods models are then compared to benchmarks widely used in the literature, such as the random walk and the Diebold and Li (2006). Main focus on this work, the NP-FDA methods didn't produce very good forecasts, being successful only for very low maturities and short forecast horizons. The forecasts generated by the FTS methods were, in general, better than our chosen benchmarks.

In the recent years, crowdfunding (a phenomenon where individuals collectively contribute money to back different goals and projects through the internet) has been gaining a lot of attention especially for its socio-economic impact. This dissertation explores this phenomenon in three distinct but related essays. The first essay explores the nature and dynamics of backers’ contributions and uses the insights generated to develop a forecasting model that can predict crowdfunding campaign outcomes. The second essay investigates how creators’ crowdfunding campaign design decisions impact their funding and post-funding outcomes. Interestingly, the essay highlights that certain crowdfunding campaign design decisions have differential effects on both funding and post-funding phases and this has implications for creators, backers, and crowdfunding platform owners. Finally, the third essay investigates whether creators’ post-funding relations-building efforts with backers matter and how such relations-building efforts might impact the performance of their subsequent crowdfunding campaign. In general, this dissertation not only increases our understanding of the crowdfunding phenomenon across the funding and post-funding phases, it also provides insights and tools that can help stakeholders maximize the benefits accruable to them when they engage in crowdfunding.

abstract: Functional regression models are widely considered in practice. To precisely understand an underlying functional mechanism, a good sampling schedule for collecting informative functional data is necessary, especially when data collection is limited. However, scarce research has been conducted on the optimal sampling schedule design for the functional regression model so far. To address this design issue, efficient approaches are proposed for generating the best sampling plan in the functional regression setting. First, three optimal experimental designs are considered under a function-on-function linear model: the schedule that maximizes the relative efficiency for recovering the predictor function, the schedule that maximizes the relative efficiency for predicting the response function, and the schedule that maximizes the mixture of the relative efficiencies of both the predictor and response functions. The obtained sampling plan allows a precise recovery of the predictor function and a precise prediction of the response function. The proposed approach can also be reduced to identify the optimal sampling plan for the problem with a scalar-on-function linear regression model. In addition, the optimality criterion on predicting a scalar response using a functional predictor is derived when the quadratic relationship between these two variables is present, and proofs of important properties of the derived optimality criterion are also provided. To find such designs, an algorithm that is comparably fast, and can generate nearly optimal designs is proposed. As the optimality criterion includes quantities that must be estimated from prior knowledge (e.g., a pilot study), the effectiveness of the suggested optimal design highly depends on the quality of the estimates. However, in many situations, the estimates are unreliable; thus, a bootstrap aggregating (bagging) approach is employed for enhancing the quality of estimates and for finding sampling schedules stable to the misspecification of estimates. Through case studies, it is demonstrated that the proposed designs outperform other designs in terms of accurately predicting the response and recovering the predictor. It is also proposed that bagging-enhanced design generates a more robust sampling design under the misspecification of estimated quantities. / Dissertation/Thesis / Doctoral Dissertation Statistics 2020

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Anterior cruciate knee ligament injuries are common and well known, especially amongst athletes.These injuries often require surgeries and long rehabilitation programs, and can lead to functionloss and re-injuries (Marshall et al., 1977). This work aims to explore the possibility of applyingsupervised classification on knee functionality, using different types of models, and testing differentdivisions of classes. The data used is gathered through a performance test, where individualsperform one-leg hops with motion sensors attached to their bodies. The obtained data representsthe position over time, and is considered functional data.With functional data analysis (FDA), a process can be analysed as a continuous function of time,instead of being reduced to finite data points. FDA includes many useful tools, but also somechallenges. A functional observation can for example be differentiated, a handy tool not found inthe multivariate tool-box. The speed, and acceleration, can then be calculated from the obtaineddata. How to define "similarity" is, on the other hand, not as obvious as with points. In this work,an FDA-approach is taken on classifying knee kinematic data, from a long-term follow-up studyon knee ligament injuries.This work studies kernel functional classifiers, and k-nearest neighbours models, and performssignificance tests on the model accuracy, using re-sampling methods. Additionally, depending onhow similarity is defined, the models can distinguish different features of the data. Attempts atutilising more information through incorporation of ensemble-methods, does not exceed the singlemodels it is created from. Further, it is shown that classification on optimised sub-domains, canbe superior to classifiers using the full domain, in terms of predictive power. / Främre korsbandsskador är vanliga och välkända skador, speciellt bland idrottsutövare. Skadornakräver ofta operationer och långa rehabiliteringsprogram, och kan leda till funktionell nedsättningoch återskador (Marshall et al., 1977). Målet med det här arbetet är att utforska möjligheten attklassificera knän utifrån funktionalitet, där utfallet är känt. Detta genom att använda olika typerav modeller, och genom att testa olika indelningar av grupper. Datat som används är insamlatunder ett prestandatest, där personer hoppat på ett ben med rörelsesensorer på kroppen. Deninsamlade datan representerar position över tid, och betraktas som funktionell data.Med funktionell dataanalys (FDA) kan en process analyseras som en kontinuerlig funktion av tid,istället för att reduceras till ett ändligt antal datapunkter. FDA innehåller många användbaraverktyg, men även utmaningar. En funktionell observation kan till exempel deriveras, ett händigtverktyg som inte återfinns i den multivariata verktygslådan. Hastigheten och accelerationen kandå beräknas utifrån den insamlade datan. Hur "likhet" är definierat, å andra sidan, är inte likauppenbart som med punkt-data. I det här arbetet används FDA för att klassificera knärörelsedatafrån en långtidsuppföljningsstudie av främre korsbandsskador.I detta arbete studeras både funktionella kärnklassificerare och k-närmsta grannar-metoder, och ut-för signifikanstest av modellträffsäkerheten genom omprovtagning. Vidare kan modellerna urskiljaolika egenskaper i datat, beroende på hur närhet definieras. Ensemblemetoder används i ett försökatt nyttja mer av informationen, men lyckas inte överträffa någon av de enskilda modellerna somutgör ensemblen. Vidare så visas också att klassificering på optimerade deldefinitionsmängder kange en högre förklaringskraft än klassificerare som använder hela definitionsmängden.

The aim of the master thesis is to review of reconstruction techniques of func- tional data and existing one-way functional ANOVA (FANOVA) tests. Specif- ically, the work deals with L2 -norm based and F-type mean functions equality tests, L2 -norm based covariance functions equality tests and tests for distri- bution equality. Furthermore, for each type of the test, it is introduced test based on reconstructed functional data, using orthornormal basis functions of L2 space. Finally, simulation study was conducted for comparing properties of tests using orthonormal basis representation of functional data and tests applied on non-reconstructed data. 1

We describe basic notions of functional random elements and the space of functions L2 [0, 1]. We discuss the non-existence of a probability density functional and the re- quirements for integrating in a functional space. In Chapter 2, we define distribution functionals and introduce a goodness-of-fit test which utilises them. The concept of char- acteristic functionals follows in Chapter 3, along with the latest test for Gaussianity of functional random elements. We conclude the chapter with our own new goodness-of- fit test, where we prove the distribution of its test statistic under the alternative, then under the null hypothesis, and lastly the distribution of the bootstrapped test statistic. Finally, we illustrate the theory on a simulation study of the empirical significance level and power of the goodness-of-fit tests. 1