In this thesis, we study statistical inference for entropy, divergence, and related functionals of one or two probability distributions. Asymptotic properties of particular nonparametric estimators of such functionals are investigated. We consider estimation from both independent and dependent observations. The thesis consists of an introductory survey of the subject and some related theory and four papers (A-D). In Paper A, we consider a general class of entropy-type functionals which includes, for example, integer order Rényi entropy and certain Bregman divergences. We propose U-statistic estimators of these functionals based on the coincident or epsilon-close vector observations in the corresponding independent and identically distributed samples. We prove some asymptotic properties of the estimators such as consistency and asymptotic normality. Applications of the obtained results related to entropy maximizing distributions, stochastic databases, and image matching are discussed. In Paper B, we provide some important generalizations of the results for continuous distributions in Paper A. The consistency of the estimators is obtained under weaker density assumptions. Moreover, we introduce a class of functionals of quadratic order, including both entropy and divergence, and prove normal limit results for the corresponding estimators which are valid even for densities of low smoothness. The asymptotic properties of a divergence-based two-sample test are also derived. In Paper C, we consider estimation of the quadratic Rényi entropy and some related functionals for the marginal distribution of a stationary m-dependent sequence. We investigate asymptotic properties of the U-statistic estimators for these functionals introduced in Papers A and B when they are based on a sample from such a sequence. We prove consistency, asymptotic normality, and Poisson convergence under mild assumptions for the stationary m-dependent sequence. Applications of the results to time-series databases and entropy-based testing for dependent samples are discussed. In Paper D, we further develop the approach for estimation of quadratic functionals with m-dependent observations introduced in Paper C. We consider quadratic functionals for one or two distributions. The consistency and rate of convergence of the corresponding U-statistic estimators are obtained under weak conditions on the stationary m-dependent sequences. Additionally, we propose estimators based on incomplete U-statistics and show their consistency properties under more general assumptions.

O objetivo desta tese é demonstrar que para um subshift de Markov topologicamente transitivo com alfabeto enumerável e um potencial &#402 com pressão de Gurevic finita e variação limitada (&#402) < &#8734, existe um único estado de equilíbrio &#181t&#402 para cada t > 1, e a família (&#181t&#402)t>1 tem um ponto de acumulação quando t > &#8734. Além disso se também supomos que o &#402 é um potencial de Markov, demonstramos que a família de estados de equilíbrio (&#181t&#402)t>1 converge quando t > &#8734. Finalmente demonstramos a continuidade em &#8734 da entropia com respeito ao parâmetro t. Estes resultados não dependem da hipótese de existência de medidas de Gibbs. / The aim of this thesis is to prove that for a topologically transitive Markov subshift with countable alphabet and a summable potential &#402 with finite topological pressure Gurevic and bounded variation (&#402) < &#8734, there exists an equilibrium state &#181t&#402 tf for each t > 1 and the family of equilibrium states (&#181t&#402)t>1 associated to each potential tf has an accumulation point at t > &#8734. Moreover if we also assume that &#402 is a Markov potential we prove that the equilibrium states family (&#181t&#402)t>1 converges when t > &#8734. Finally we prove the continuity at &#8734 of the entropy with respect to the parameter t. These results do not depend on assuming the existence of Gibbs measures.

<p>Studiens första syfte är att med institutionell teori kartlägga det kontraktsnät som konstituerar den europeiska marknaden för professionella herrgolfare. Det andra syftet är att analysera och diskutera vissa utvalda aspekter av detta kontraktsnät som utmärker Europatouren från traditionella vinstmaximerande företag. </p><p>Den europeiska marknaden för proffsgolfare har organiserats i ett företag för att det är ekonomiskt fördelaktigt. Med Europatouren som en sammanhållande länk begränsas transaktionskostnaderna bl.a. genom att antalet kontraktsvägar reduceras och genom att utrymme för långsiktiga relationer med viktiga parter skapas. </p><p>Europatourens prissummemaximerande huvudmål förenar och tjänar de flesta, om inte samtliga,intressenters delmål i kontraktsnätet. I ambitionen att tillfredsställa alla intressenter har en gigantisk institutionsapparat formats på Europatouren. Institutionernas uppgift är att hålla tillbaka transaktionskostnaderna, motverka ett opportunistiskt beteende hos spelarna och bevara sportens konformitet och gentlemannaapproach. </p><p>Stjärnspelarna är de som gör Europatouren attraktiv och för att lyckas behålla dem i den konkurrens man möter från USA-touren har ett favoriseringssystem skapats som innebär att de erhåller appearance money och bättre service. Förekomsten av appearance money berättigas av deras viktiga funktioner i kontraktsnätet. </p><p>Flera faktorer pekar på att ett icke traditionellt riskförhållande råder på en proffstour för golf, d.v.s. att spelaren (agenten) är riskbenägen och att Europatouren (principalen) är riskneutral. Med föreliggande riskförhållande skapas drivkrafter hos spelarna att alltid göra sitt yttersta på träning och tävling, och begränsas utrymmet för opportunistiskt beteende. Dessa faktorer ger en högkvalitativ tour, vilket är nödvändigt för att alla involverade intressenters mål ska bli uppfyllda.</p> / <p>The first object of this study is to, with institutional theory, map out the nexus of contracts which constitutes the European market for professional male golfers. The second object is to analyze and discuss some chosen aspects of this nexus of contracts which characterize the European Tour in comparison with traditional profit-maximizing firms. </p><p>The European market for professional golfers has been organized as a firm because of more economically favourable reasons. With the European Tour as a connecting link the transaction costs are lowered among other things, by the fact that the number of contract ways is reduced and that room for long-term relationships with important parties is created. </p><p>The price money maximizing purpose of the European Tour unite and serve most, if not all, intermediate aims of the parties included in the nexus of contracts. In the ambition to satisfy all parties a huge formal and informal apparatus of institutions has been formedon the European Tour. The task of the institutions is to reduce transaction costs, to counteract opportunistic behaviour from the players and to preserve the conformity and the gentlemanlike approach of the sport. </p><p>The star players are what makes the European Tour attractive and to be able to keep them in the competition with the USA Tour a favouring system has been created, which implies that they receive appearance money and better service. The occurrence of appearance money is justified by the players’ importance in the nexus of contracts. </p><p>Many factors indicate that there is no traditional risk relationship on a professional tour for golf. That is, the player (the agent) is risk loving while the European Tour (the principal) is risk neutral. With the existing risk relationship driving forces are created in the players to always perform their utmost during training and competition, and opportunistic behaviour is thereby restricted. These factors give a high-quality tour, which is necessary for the goals of all involved parties will be reached.</p>

Studiens första syfte är att med institutionell teori kartlägga det kontraktsnät som konstituerar den europeiska marknaden för professionella herrgolfare. Det andra syftet är att analysera och diskutera vissa utvalda aspekter av detta kontraktsnät som utmärker Europatouren från traditionella vinstmaximerande företag. Den europeiska marknaden för proffsgolfare har organiserats i ett företag för att det är ekonomiskt fördelaktigt. Med Europatouren som en sammanhållande länk begränsas transaktionskostnaderna bl.a. genom att antalet kontraktsvägar reduceras och genom att utrymme för långsiktiga relationer med viktiga parter skapas. Europatourens prissummemaximerande huvudmål förenar och tjänar de flesta, om inte samtliga,intressenters delmål i kontraktsnätet. I ambitionen att tillfredsställa alla intressenter har en gigantisk institutionsapparat formats på Europatouren. Institutionernas uppgift är att hålla tillbaka transaktionskostnaderna, motverka ett opportunistiskt beteende hos spelarna och bevara sportens konformitet och gentlemannaapproach. Stjärnspelarna är de som gör Europatouren attraktiv och för att lyckas behålla dem i den konkurrens man möter från USA-touren har ett favoriseringssystem skapats som innebär att de erhåller appearance money och bättre service. Förekomsten av appearance money berättigas av deras viktiga funktioner i kontraktsnätet. Flera faktorer pekar på att ett icke traditionellt riskförhållande råder på en proffstour för golf, d.v.s. att spelaren (agenten) är riskbenägen och att Europatouren (principalen) är riskneutral. Med föreliggande riskförhållande skapas drivkrafter hos spelarna att alltid göra sitt yttersta på träning och tävling, och begränsas utrymmet för opportunistiskt beteende. Dessa faktorer ger en högkvalitativ tour, vilket är nödvändigt för att alla involverade intressenters mål ska bli uppfyllda. / The first object of this study is to, with institutional theory, map out the nexus of contracts which constitutes the European market for professional male golfers. The second object is to analyze and discuss some chosen aspects of this nexus of contracts which characterize the European Tour in comparison with traditional profit-maximizing firms. The European market for professional golfers has been organized as a firm because of more economically favourable reasons. With the European Tour as a connecting link the transaction costs are lowered among other things, by the fact that the number of contract ways is reduced and that room for long-term relationships with important parties is created. The price money maximizing purpose of the European Tour unite and serve most, if not all, intermediate aims of the parties included in the nexus of contracts. In the ambition to satisfy all parties a huge formal and informal apparatus of institutions has been formedon the European Tour. The task of the institutions is to reduce transaction costs, to counteract opportunistic behaviour from the players and to preserve the conformity and the gentlemanlike approach of the sport. The star players are what makes the European Tour attractive and to be able to keep them in the competition with the USA Tour a favouring system has been created, which implies that they receive appearance money and better service. The occurrence of appearance money is justified by the players’ importance in the nexus of contracts. Many factors indicate that there is no traditional risk relationship on a professional tour for golf. That is, the player (the agent) is risk loving while the European Tour (the principal) is risk neutral. With the existing risk relationship driving forces are created in the players to always perform their utmost during training and competition, and opportunistic behaviour is thereby restricted. These factors give a high-quality tour, which is necessary for the goals of all involved parties will be reached.

O objetivo desta tese é demonstrar que para um subshift de Markov topologicamente transitivo com alfabeto enumerável e um potencial &#402 com pressão de Gurevic finita e variação limitada (&#402) < &#8734, existe um único estado de equilíbrio &#181t&#402 para cada t > 1, e a família (&#181t&#402)t>1 tem um ponto de acumulação quando t > &#8734. Além disso se também supomos que o &#402 é um potencial de Markov, demonstramos que a família de estados de equilíbrio (&#181t&#402)t>1 converge quando t > &#8734. Finalmente demonstramos a continuidade em &#8734 da entropia com respeito ao parâmetro t. Estes resultados não dependem da hipótese de existência de medidas de Gibbs. / The aim of this thesis is to prove that for a topologically transitive Markov subshift with countable alphabet and a summable potential &#402 with finite topological pressure Gurevic and bounded variation (&#402) < &#8734, there exists an equilibrium state &#181t&#402 tf for each t > 1 and the family of equilibrium states (&#181t&#402)t>1 associated to each potential tf has an accumulation point at t > &#8734. Moreover if we also assume that &#402 is a Markov potential we prove that the equilibrium states family (&#181t&#402)t>1 converges when t > &#8734. Finally we prove the continuity at &#8734 of the entropy with respect to the parameter t. These results do not depend on assuming the existence of Gibbs measures.

Abstract The focus of the thesis is researching how to optimize a certain route, highlighting theimportance of weather conditions in the context of optimizing truck routes. Additionally, itemphasizes the goals of maximizing human utilization and cost-effectiveness. The project teamconducted a survey on fuel habits, and the results showed that the participating companies lackeda defined strategy for the company's fuel habits or a specific approach for selecting fuelingcompanies. The project team developed an algorithm that assists drivers in selecting the mostoptimized routes while enabling companies to calculate these routes efficiently. Data wascollected on the fuel consumption associated with the loading and unloading of goods. The totalroute cost is calculated using a custom equation that includes the driver´s salary, the employer´ssocial security contribution, the cost of the truck when loading and unloading, and the wear onthe truck. The company naturally expects to generate a profit, and such profit margins may differamong companies. Therefore, the project team excluded this factor from the equation todetermine the route's cost. The findings showed that varying weather conditions did impactconsumption, thereby influencing the final cost. The algorithm that the project team made is asignificant milestone toward the completion of the final product. However, there are still a fewremaining steps to be taken in order to achieve the desired end result and future development.