This thesis is concerned with data analysis, especially with principal component analysis and its sparse modi cation (SPCA), which is NP-hard-to- solve. SPCA problem can be recast into the regression framework in which spar- sity is usually induced with ℓ1-penalty. In the thesis, we propose to use iteratively reweighted ℓ2-penalty instead of the aforementioned ℓ1-approach. We compare the resulting algorithm with several well-known approaches to SPCA using both simulation study and interesting practical example in which we analyze voting re- cords of the Parliament of the Czech Republic. We show experimentally that the proposed algorithm outperforms the other considered algorithms. We also prove convergence of both the proposed algorithm and the original regression-based approach to PCA. vi

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Cette recherche vise à comprendre la relation existante entre l’innovation de services et l’internationalisation, à savoir, comment les entreprises obtiennent des avantages compétitifs sur les marchés internationaux grâce à l'innovation dans le secteur des services aux entreprises.Nous avons testé la relation entre l'innovation et la performance internationale, avons évalué l'impact de l'innovation par rapport à d'autres avantages internationaux. Symétriquement, nous avons également vérifié dans quelle mesure le processus d'internationalisation peut être un puissant moteur d'innovation pour les entreprises de services. Après le développement d'un modèle théorique, nous avons procédé à une enquête téléphonique auprès de 807 entreprises de services exportatrices. Les répondants cible de l'enquête étaient des cadres supérieurs de sociétés de services internationalisés en France. 51 réponses exploitables ont été reçues. Les données recueillies ont été analysées par Modélisation des Équations Structurelles (SEM), en utilisant la méthode Partial Least Square. Le modèle testé montre que l'innovation de service a une influence positive sur le développement international et que la compétence internationale, obtenue sur les marchés étrangers, stimule la dynamique de l'innovation dans les entreprises de services. Le modèle proposé met en évidence les capacités de R & D (organisationnelle), relationnelles, les TIC, la compétence internationale, l’innovation de service et l’expérience internationale comme facteurs qui influent les résultats des entreprises internationalisées, ou plus précisément, la performance international. / This research deals with service innovation and internationalization: how firms perform on international markets and get an edge thanks to innovation on service concept or service process. We tested the relationship between innovation and international performance, assessed the impact of innovation compared to other international advantages. Symmetrically, we also checked how far the internationalization process can be a powerful driver of innovation for service firms. After the development of a theoretical model, data were collected from a telephone survey. The target respondents of the survey were senior executives of internationalized service companies in France. Out of the 807 companies which were contacted, 51 usable responses were received. The data collected were analyzed by Structural Equation Modeling (SEM), using the Partial Least Square method. The tested model shows that service innovation has a positive influence on international development and that the international competence, obtained in foreign markets, drives the dynamics of innovation in services company. The model proposed highlights the capabilities for R & D (organizational), relational, ICT, international competence, service and international experience as factors that impact the final results of internationalized companies, or more specifically, the international performance.

This diploma thesis examines various linear regression methods and their use to establish regression relationships between the compressive strength of concrete determined by the indirect method and by the crushing of the specimens in the press. It deals mainly with the uncertainty of values measured by the indirect method, which is neglected by the usually used ordinary least squares regression method. It also deals with the weighted least squares method, suitable for so-called heteroskedastic data. It compares different regression methods on several sets of previously measured data. The final part of the work examines the effect of removing too influential points identified by Cook's distance, which may skew the regression results.

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Det finns olika aspekter som påverkar den ekonomiska tillväxten, där ibland inflation. Det har under många år pågått diskussioner om hur förhållandet mellan dessa två variabler ser ut. Denna uppsats analyserar sambandet mellan ekonomisk tillväxt och inflation. Utöver detta besvarar studien om inflation har någon statistisk signifikant relation till den ekonomiska tillväxten. I studien används paneldata från 19 OECD-medlemsländer från 1976 till 2020. För att analysera data utformas en regressionsmodell genom att använda BNP per capita som beroende variabel samt inkludera sju oberoende variabler (inflation, utländska direktinvesteringar, inhemska sparande, bytesvillkor, befolkningstillväxt, humankapital samt initial BNP). Resultatet från regressionsanalysen som utfördes genom fixed effects least squares dummy variable modellen tyder på ett negativt samband mellan inflation och BNP per capita. Däremot är resultatet enbart statistiskt signifikant om inte länder-, perioddummies eller initial BNP inkluderas. / There are various aspects that affect economic growth, including inflation. For many years, there have been discussions about the relationship between these two variables. This thesis analyzes the relation between economic growth and inflation. In addition, the study answers whether inflation has any statistically significant relation to economic growth. The study uses panel data from 19 OECD member countries from 1976 to 2020. To analyze the data, a regression model is designed by using ln GDP per capita as a dependent variable and including seven independent variables (inflation, foreign direct investment, domestic savings, terms of trade, population growth, human capital and initial GDP). The results of the regression analysis are conducted using the fixed effects least squares dummy variable model indicate a negative relationship between inflation and GDP per capita. However, the result is only shown to be statistically significant unless countries-, period dummies or initial GDP are included.

The purpose of this thesis is to predict the lifespan of a battery using a predictive model, utilizing data from early cycles. The goal is to minimize both time and costs for the company by reducing the number of cycles needed for testing. Currently, the company tests a diverse set of batteries, which is both time and resource-consuming. To investigate which data-driven predictive model should be used by the company to predict battery capacity at XX cycles, a thorough literature study has been conducted. In summary, a variety of variables from specific cycles have been calculated based on inspiration from Fei et al. (2021), Severson et al. (2019), Enholm et al. (2022) and an internal project from the company. Following this, two different predictive models, Gaussian Process Regression and Ordinary Least Squared Regression, are applied and compared.  Based on the obtained results, Gaussian Process Regression had a slight better results but a significantly higher complexity compared to Ordinary Least Squared Regression. Therefore, the data-driven model that should be implemented at the company is an Ordinary Least Squared Regression with variables related to different phases during a cycle. This result is primarily based on the varying degrees of complexity of the models. / Syftet med detta examensarbete är att med hjälp av en datadriven prediktionsmodell kunna prediktera livslängden på ett batteri genom att använda data från tidiga cykler. Målet är att minimera både tid och kostnader för företaget genom att minska antalet cykler som behövs för testning. I dagsläget testar företaget en mängd batterier vilket både är tids- samt resurskrävande. För att undersöka vilken datadriven prediktionsmodell som bör användas av företaget för att prediktera batteriekapacitet vid XX cykler har en gedigen litteraturstudie utförts. Sammanfattningsvis har en mängd variabler av de mätningar som finns från specifika cykler beräknats utifrån inspiration från Fei med flera (2021), Severson med flera (2019), Enholm med flera (2022) samt ett internt projekt från företaget. Efter detta applicerades och jämfördes två olika prediktionsmodeller: Gaussian Process Regression och Ordinary Least Squared Regression.  Baserat på de erhållna resultaten hade Gaussian Process Regression något bättre resultat men en betydligt högre komplexitet jämfört med Ordinary Least Squared Regression. Därför är den datadrivna modell som bör implementeras på företaget en Ordinary Least Squared Regression med variabler relaterade till olika faser under en cykel. Detta resultat grundar sig framför allt i olika grad av komplexitet hos modellerna.

Markets increase social welfare by matching willing buyers and sellers. It is important to understand whether markets are fulfilling their societal purpose and are operating efficiently. The prevalence of spatial arbitrage in markets is an important indicator of market efficiency. The two essays in my dissertation study spatial arbitrage and the behaviors of arbitrageurs Electronic commerce can improve market efficiency by helping buyers and sellers find and transact with each other across geographic distance. In the first essay, we study the effect of two distinct forms of electronic commerce on market efficiency, which we measure via the prevalence of spatial arbitrage. Spatial arbitrage is a more precise measure than price dispersion, which is typically used, because it accounts for the transaction costs of trading across distance and for unobserved product heterogeneity. Studying two forms of electronic commerce allows us to examine how the theoretical mechanisms of expanded reach and transaction immediacy affect market efficiency. We find that electronic commerce reduces the number of arbitrage opportunities but improves arbitrageur’s ability to identify and exploit those that remain. Overall, our results provide a novel and nuanced understanding of how electronic commerce improves market efficiency. Studying arbitrageur strategies will help us understand how arbitrageur behaviors impact markets by increasing/reducing spatial arbitrage. In the second essay, we study specialization strategies of arbitrageurs. Arbitrageurs specialize on asset type and sourcing locations. We investigate the role of specialization and find that specialization affects both arbitrage profits and arbitrage intensity. Subsequently, we find that specialization strategies evolve over time and different groups of arbitrageurs adapt differently based on behavioral biases and environmental factors. Overall, our findings support the predictions of the adaptive markets hypothesis and help us understand antecedents such as capital, arbitrage intensity, etc. which affect the evolution of arbitrageur strategy.

Master of Science / Department of Statistics / Paul I. Nelson / The principle of least squares applied to regression models estimates parameters by minimizing the mean of squared residuals. Least squares estimators are optimal under normality but can perform poorly in the presence of outliers. This well known lack of robustness motivated the development of alternatives, such as least median of squares estimators obtained by minimizing the median of squared residuals. This report uses simulation to examine and compare the robustness of least median of squares estimators and least squares estimators of the slope of a regression line through the origin in terms of bias and mean squared error in a variety of conditions containing outliers created by using mixtures of normal and heavy tailed distributions. It is found that least median of squares estimation is almost as good as least squares estimation under normality and can be much better in the presence of outliers.