The social welfare of an economy is maximized when the various economic industries operate under conditions of perfect competition. According to the industrial organization, any deviation from perfect competition leads to several losses for the economy and more generally for the society. The investigation of the degree of market power, which comprises the basic objective of the present dissertation, is vital for the proper functioning of the economy. Therefore, the present study tests for the degree of market power and the market power determinants in the twenty-one sectors of the Greek manufacturing industry over the period 1983-2007. The degree of market power is also assessed in the nine sectors of the Greek food and beverages manufacturing industry for the period 1983-2007. Moreover, this study investigates the markup and the markup determinants for the twenty-one sectors of the Greek manufacturing industry as well as for the nine sectors of the Greek food and beverages manufacturing industry over the period 1984-2007. Furthermore, the present study estimates the welfare losses in the event of the existence of oligopoly power. In addition, the technical efficiency and its determinants are investigated for the twenty-one sectors of the Greek manufacturing industry as well as for the nine sectors of the Greek food and beverages manufacturing industry during the period 1984-2007. Three different approaches based on the “new empirical industrial organization” (NEIO) were used with the view to measuring the degree of market power and evaluating the competitive conditions. The first approach is the conjectural variation approach, which provides estimates regarding the actual degree of market power. The second approach is the Hall-Roeger approach and it investigates the market structure and more specifically the markup. The third approach developed comprises an extension of the Hal-Roeger approach and offers contemporaneous estimates about the degree of market power and the markup. Moreover, the welfare losses were estimated using a formal model of oligopoly. The technical efficiency was measured following the “data envelopment analysis” (DEA), while its sources were determined based on the Simar and Wilson’s Algorithm 1. A very important issue in the present study is the application of the bootstrap technique to the empirical estimations. That is why the application of the bootstrapping can lead to an accurate estimation of the sampling distribution without any assumptions on the distribution of the population from which the sample was taken so that the results of the empirical estimates can be accurate, robust and reliable. The empirical results indicate the presence of some degree of market power and markup in all sectors of the Greek manufacturing industry as well as those of the Greek food and beverages manufacturing industry over the period 1983-2007. In other words, the findings imply that both the manufacturing industry as well as the food and beverages industry operated under conditions of imperfect competition implying the existence of welfare losses. Furthermore, the results indicate that in the case of the Greek manufacturing industry, among the factors determining the market power and the markup at the sectoral level are the number of firms, the labor intensity and the sector size, while the determinants of market power and markup, over time, are the number of firms, the labor intensity and the growth. In the case of the Greek food and beverages manufacturing industry, the results suggest that among the determinants of the markup are the number of firms, the capital intensity and the sector size. More specifically, the empirical results imply that the degree of market power and the markup are negatively related to the variables of the number of firms and the labor intensity. In other words, the higher the number of firms, the lower the degree of market power and markup. Also, the sectors which are more labor-intensive have a lower degree of market power and markup. Additionally, the findings support that the degree of market power and the markup are related positively to the variables of the sector size, the growth and the capital intensity. In particular, the bigger the size of a sector the higher the degree of market power and markup. Also, the growth leads to a higher level of market power and markup. Furthermore, the sectors which are more capital-intensive have a higher markup. Moreover, the empirical results indicate that, on average, all sectors of the Greek manufacture as well as those of the food and beverages industry are technically inefficient over the period 1984-2007. Note that, in the case of the Greek manufacturing industry, the technical efficiency tends to increase over the period 1984-2007, whereas in the case of the Greek food and beverages manufacturing industry, the technical efficiency tends to decrease over the same period, i.e. 1984-2007. Also, the findings of the present dissertation imply that among the factors affecting technical efficiency for both the Greek manufacture and the food and beverages industry are the sector size, the growth, the capital and labor productivity and the labor intensity. More specifically, the empirical results indicate that the variables of sector size, growth, capital and labor productivity and labor intensity can positively influence the level of technical efficiency. In other words, the bigger the sector the higher the level of technical efficiency. Also, the growth improves the technical efficiency of a sector. Moreover, an increase in the capital productivity or/and in the labor productivity can lead to a higher level of technical efficiency. In addition to that, an increase of the labor intensity can result in the technical efficiency increase. / Η κοινωνική ευημερία μιας οικονομίας μεγιστοποιείται όταν οι διάφοροι κλάδοι που την απαρτίζουν λειτουργούν ανταγωνιστικά. Σύμφωνα με τη βιομηχανική οργάνωση, οποιαδήποτε απόκλιση από τον τέλειο ανταγωνισμό οδηγεί σε διάφορες απώλειες για την εν λόγω οικονομία, οι οποίες βέβαια επιφέρουν και ποικίλες κοινωνικές επιπτώσεις. Η εξέταση του βαθμού δύναμης της αγοράς (market power), η οποία αποτελεί τον βασικό στόχο της παρούσας διατριβής, είναι ζωτικής σημασίας για την σωστή λειτουργία της οικονομίας. Στο πλαίσιο της παρούσας διδακτορικής διατριβής πραγματοποιείται μία προσπάθεια εκτίμησης του βαθμού δύναμης της αγοράς (market power) και των προσδιοριστικών της παραγόντων για είκοσι-ένα (21) κλάδους της ελληνικής μεταποιητικής βιομηχανίας χρησιμοποιώντας στοιχεία της περιόδου 1983-2007. Επιπλέον, στόχος της εργασίας αυτής είναι ο υπολογισμός του βαθμού δύναμης της αγοράς (market power) των εννέα (9) κλάδων της ελληνικής βιομηχανίας τροφίμων και ποτών κατά τη διάρκεια της περιόδου 1983-2007. Επίσης, υπολογίζεται το περιθώριο κέρδους (markup) και οι προσδιοριστικοί του παράγοντες για τους είκοσι-ένα κλάδους της ελληνικής μεταποιητικής βιομηχανίας και τους εννέα κλάδους της ελληνικής βιομηχανίας τροφίμων και ποτών κατά τη διάρκεια της περιόδου 1984-2007, καθώς και οι απώλειες ευημερίας σε περίπτωση ύπαρξης ολιγοπωλιακής δύναμης στους εν λόγω κλάδους. Τέλος, στο πλαίσιο της εργασίας αυτής γίνεται υπολογισμός του επιπέδου τεχνικής αποτελεσματικότητας καθώς και των προσδιοριστικών παραγόντων της τεχνικής αποτελεσματικότητας για τους είκοσι-ένα κλάδους της ελληνικής μεταποιητικής βιομηχανίας και τους εννέα κλάδους της ελληνικής βιομηχανίας τροφίμων και ποτών κατά τη διάρκεια της περιόδου 1984-2007. Τρεις διαφορετικές προσεγγίσεις, που βασίζονται στην μεθοδολογία της «νέας εμπειρικής βιομηχανικής οργάνωσης», χρησιμοποιούνται για την μέτρηση του βαθμού δύναμης της αγοράς (market power) και την εξέταση των συνθηκών ανταγωνισμού γενικότερα. Η πρώτη, αφορά την προσέγγιση της «εικαζόμενης μεταβλητότητας» και παρέχει εκτιμήσεις σχετικά με τον ακριβή βαθμό δύναμης της αγοράς (market power). Η δεύτερη, βασίζεται στην προσέγγιση των Hall-Roeger και εξετάζει τη δομή της αγοράς και πιο συγκεκριμένα το περιθώριο κέρδους (markup). Η τρίτη προσέγγιση που αναπτύσσεται αποτελεί μια επέκταση της προσέγγισης των Hal-Roeger και παρέχει ταυτόχρονες εκτιμήσεις σχετικά με το βαθμό δύναμης της αγοράς και το περιθώριο κέρδους. Μέσω της παρούσας εργασίας, επίσης, γίνεται προσπάθεια εκτίμησης των απωλειών ευημερίας χρησιμοποιώντας ένα τυπικό μοντέλο ολιγοπωλίου. Επιπλέον, μετράται η τεχνική αποτελεσματικότητα ακολουθώντας την τεχνική της «περιβάλλουσας ανάλυσης δεδομένων» (data envelopment analysis or DEA), ενώ οι παράγοντες που την επηρεάζουν προσδιορίζονται βάσει του Αλγορίθμου 1 των Simar and Wilson. Ένα πολύ σημαντικό σημείο αυτής της διατριβής αποτελεί η εφαρμογή της μεθόδου «bootstrap» στις εμπειρικές εκτιμήσεις. Το παραπάνω παρουσιάζει ιδιαίτερο ενδιαφέρον, γιατί η εφαρμογή της συγκεκριμένης μεθόδου μπορεί να οδηγήσει στην ακριβή εκτίμηση της δειγματικής κατανομής χωρίς καμία υπόθεση για την κατανομή του πληθυσμού από τον οποίο λαμβάνεται το δείγμα ούτως ώστε τα αποτελέσματα των εμπειρικών εκτιμήσεων να είναι ιδιαίτερα αξιόπιστα. Τα εμπειρικά αποτελέσματα αναδεικνύουν τόσο την παρουσία κάποιου βαθμού δύναμης της αγοράς όσο κι ενός περιθωρίου κέρδους σε όλους τους κλάδους της ελληνικής μεταποιητικής βιομηχανίας και της ελληνικής βιομηχανίας τροφίμων και ποτών κατά την διάρκεια της περιόδου 1983-2007. Γενικά, τα αποτελέσματα δείχνουν ότι και η μεταποιητική βιομηχανία και η βιομηχανία τροφίμων και ποτών λειτουργούν υπό συνθήκες ατελούς ανταγωνισμού έχοντας ως συνέπεια την ύπαρξη απωλειών ευημερίας για τους εν λόγω κλάδους. Επιπλέον, στην περίπτωση της ελληνικής μεταποιητικής βιομηχανίας, ανάμεσα στους παράγοντες που επηρεάζουν τη δύναμη της αγοράς και το περιθώριο κέρδους σε επίπεδο κλάδου είναι ο αριθμός των επιχειρήσεων, η μεταβλητή εντάσεως εργασίας και το μέγεθος του κλάδου, ενώ ανάμεσα στους προσδιοριστικούς παράγοντες της δύναμης της αγοράς και του περιθωρίου κέρδους διαχρονικά συγκαταλέγονται ο αριθμός των επιχειρήσεων, η μεταβλητή εντάσεως εργασίας και η ανάπτυξη. Στην περίπτωση της ελληνικής βιομηχανίας τροφίμων και ποτών τα εμπειρικά αποτελέσματα δείχνουν ότι ανάμεσα στους προσδιοριστικούς παράγοντες του περιθωρίου κέρδους είναι ο αριθμός των επιχειρήσεων, η μεταβλητή εντάσεως κεφαλαίου και το μέγεθος του κλάδου. Πιο συγκεκριμένα, τα εμπειρικά αποτελέσματα φανερώνουν ότι ο βαθμός δύναμης της αγοράς και το περιθώριο κέρδους είναι μεγέθη αντιστρόφως ανάλογα του αριθμού των επιχειρήσεων και της μεταβλητής εντάσεως εργασίας. Κατά συνέπεια, όσο μεγαλύτερος είναι ο αριθμός των επιχειρήσεων σε ένα κλάδο, τόσο χαμηλότερος είναι ο βαθμός δύναμης της αγοράς και το περιθώριο κέρδους. Επίσης, οι κλάδοι που είναι περισσότερο εντάσεως εργασίας έχουν χαμηλότερο βαθμό δύναμης της αγοράς και περιθώριο κέρδους. Ένα επιπρόσθετο συμπέρασμα που εξάγεται μέσα από τη μελέτη και την ερμηνεία των εμπειρικών αποτελεσμάτων είναι ότι ο βαθμός δύναμης της αγοράς και το περιθώριο κέρδους σχετίζονται θετικά με το μέγεθος του κλάδου, την ανάπτυξη και τη μεταβλητή εντάσεως κεφαλαίου. Πιο συγκεκριμένα, όσο μεγαλύτερο είναι το μέγεθος του κλάδου, τόσο μεγαλύτερα είναι η δύναμη της αγοράς και το περιθώριο κέρδους. Επίσης, χρήσιμο συμπέρασμα της ερμηνείας των εμπειρικών αποτελεσμάτων είναι το ότι η ανάπτυξη φαίνεται να οδηγεί σε υψηλότερο επίπεδο δύναμης της αγοράς και περιθώριο κέρδους. Ακόμα, οι κλάδοι που είναι περισσότερο εντάσεως κεφαλαίου εμφανίζονται να έχουν υψηλότερο περιθώριο κέρδους. Σε ό,τι αφορά την παράμετρο της τεχνικής αποτελεσματικότητας τα αποτελέσματα της παρούσας διατριβής δείχνουν ότι - κατά μέσο όρο - όλοι οι κλάδοι της ελληνικής μεταποίησης και της ελληνικής βιομηχανίας τροφίμων και ποτών είναι τεχνικά αναποτελεσματικοί κατά τη διάρκεια της περιόδου 1984-2007. Ωστόσο, στην περίπτωση της ελληνικής μεταποιητικής βιομηχανίας, και για την προαναφερθείσα χρονική περίοδο, η συγκεκριμένη παράμετρος παρουσιάζει μία πτωτική τάση, ενώ στην περίπτωση της ελληνικής βιομηχανίας τροφίμων και ποτών η τάση αυτή είναι αυξητική. Επιπλέον, η αξιολόγηση των αποτελεσμάτων της παρούσας εργασίας φανερώνει ότι, τόσο για την ελληνική μεταποίηση όσο και τη βιομηχανία τροφίμων και ποτών, ανάμεσα στους παράγοντες που επηρεάζουν την τεχνική αποτελεσματικότητα είναι το μέγεθος του κλάδου, η ανάπτυξη, η παραγωγικότητα του κεφαλαίου και της εργασίας καθώς και η μεταβλητή εντάσεως εργασίας. Πιο συγκεκριμένα, μπορεί μέσω των αποτελεσμάτων να υποστηριχθεί ότι οι προαναφερθείσες μεταβλητές - το μέγεθος του κλάδου, η ανάπτυξη, η παραγωγικότητα του κεφαλαίου και της εργασίας και η μεταβλητή εντάσεως εργασίας - επηρεάζουν θετικά την τεχνική αποτελεσματικότητα. Με άλλα λόγια, μια αύξηση στο μέγεθος ενός κλάδου θα οδηγήσει σε υψηλότερο επίπεδο τεχνικής αποτελεσματικότητας. Επίσης, η ανάπτυξη βελτιώνει την τεχνική αποτελεσματικότητα ενός κλάδου. Επιπρόσθετα, μια αύξηση της παραγωγικότητας του κεφαλαίου ή/και της εργασίας μπορεί να οδηγήσει σε υψηλότερα επίπεδα τεχνικής αποτελεσματικότητας. Τέλος, μια αύξηση της μεταβλητής εντάσεως εργασίας μπορεί να οδηγήσει σε αύξηση της τεχνικής αποτελεσματικότητας.

Η παρούσα διπλωματική εργασία πραγματεύεται την μελέτη της μεθόδου Bootstrap στα πλαίσια συμπλήρωσης των ελλείψεων της DEA, κατά τον υπολογισμό της τεχνικής αποτελεσματικότητας διαφόρων μονάδων λήψης αποφάσεων. Πιο συγκεκριμένα θα μελετηθεί η Bootstrap ως μέσο για τον υπολογισμό της μεροληψίας, και διαστημάτων εμπιστοσύνης των efficiency scores που προκύπτουν από την χρήση της DEA. Όπως θα φανεί, η DEA, ως μία εφαρμογή του γραμμικού προγραμματισμού, αποτελεί μία μη παραμετρική μέθοδο υπολογισμού της τεχνικής αποτελεσματικότητας και χαρακτηρίζεται από το μειονέκτημα της έλλειψης στατιστικών μεγεθών καθώς και την αδυναμία να ξεχωρίσει τον θόρυβο από την αναποτελεσματικότητα. Η Bootstrap από την άλλη, αποτελεί μία επαναληπτική εφαρμογή της DEA, η οποία καλείται να δώσει λύση στα παραπάνω προβλήματα. Σκοπός της παρούσας διπλωματικής είναι να ελέγξει τον βαθμό στον οποίο η Bootstrap καταφέρνει να εκπληρώσει αυτή την αποστολή. Για το σκοπό αυτό χρησιμοποιούνται πραγματικά δεδομένα που αφορούν ιχθυοκαλλιέργειες που δραστηριοποιούνται στην ελληνική επικράτεια, ενώ οι υπολογισμοί γίνονται μέσω των προγραμμάτων DEAP και PIM – DEA v2.0. / The present diplomatic essay treats the study of Bootstrap method within the bounds of completion of DEA deficiencies during the estimation of technical efficiency of several decision-making units. More precisely it will be scrutinized bootstrap as a mean of estimating biasness and the confidence intervals of the efficiency scores, which arise from the use of DEA. As it will be come clear, DEA as an implementation of linear programming, constitutes a non-parametric method of estimating technical efficiency and is characterized by the drawback of non-distinguishing the noise by the inefficiency. On the other hand, bootstrap constitutes a repetitive implementation of DEA, which is assigned to give a solution to the above questions. The purpose of this essay is to verify the degree in which bootstrap completes this mission. For this reason there are used real data, which concern fish farms that are placed in Greek territory while, the calculations are executed through the programs DEAP and PIM – DEA V2.0

Le modèle du tas de sable est un modèle de diffusion discret et isotrope introduit par les physiciens Bak, Tang et Wiesenfeld comme illustration de la criticalité auto-organisée. Pour tout graphe, souvent supposé fini, Dhar a formalisé de nombreuses propriétés simplifiant son analyse. Cette thèse propose des études de ce modèle sur la grille bidimensionnelle usuelle et certains de ses sous-graphes également infinis que sont les bandes bi-infinies de hauteur finie. Des approximations du comportement de la pile de sable peuvent se rapprocher de certains modèles de bootstrap percolation avec un support de stabilisation rectangulaire. Les lois sur son demi-périmètre peuvent se décrire à l’aide de statistiques sur les permutations. Un sous-produit de ce travail fait apparaître une différence de deux séries génératrices comptant des permutations selon deux statistiques mahoniennes classiques dont est extrait un polynôme à coefficients entiers et surtout positifs. La suite de cette thèse revisite dans le cadre de ces graphes infinis, des structures jusque-là bien définies uniquement dans le cas des graphes finis, notamment la récurrence. Dans le modèle sur une bande de hauteur finie H, l’existence donnée par Járai et Lyons d’automates finis reconnaissant les configurations récurrentes lues colonne par colonne est étendu par une construction explicite d’automates avec un nombre moindre d’états, se rapprochant de la conjecture de Gamlin. Dans une seconde approche, l’étude se concentre sur les configurations sur la grille entière qui sont périodiques dans les deux directions. Le puits, un sommet du graphe garantissant la terminaison de la stabilisation, est placé à l’infini dans une direction de pente rationnelle. Ceci permet à la fois de préserver la bipériodicité et de proposer une forme affaiblie du critère de Dhar caractérisant ainsi par un algorithme effectif les configurations récurrentes. Ces configurations récurrentes bipériodiques sont des candidates naturelles pour être les éléments de sous-groupes finis de l’éventuel groupe du tas de sable sur la grille. Des éléments de construction de cette loi de groupe donnent expérimentalement quelques sous-groupes finis. / The sandpile model is a discrete model for diffusion of grains on a graph introduced by physicists Bak, Tang and Wiesenfeld as an illustration for self-organised criticality. For any finite graph, Dhar identified many of its numerous structures which simplify its analysis. This thesis focus on the usual square lattice and its subgraphs which are strips of height H, both notions of infinite graphs. Approximations on the behaviour of the stabilisation of a large stack of grains at the origin of the square lattice lead to some random distribution of grains, which stabilisation is connected to some models of bootstrap percolation where modified vertices by this stabilisation forms a rectangle. The laws of the half-perimeter of this rectangle are described by statistics on permutations. As a byproduct, the difference between the generating functions over some permutations of two classical mahonian statistics on permutations appears to mainly be a polynomial with coefficients which are integers and especially positive. Then, this thesis visits in the case of the studied infinite graphs some well-defined structures on finite graphs, in particular the recurrence. In the model on an horizontal strip of height H, we extend the existence of finite automata recognizing recurrent configurations read column by column presented by Járai and Lyons to new automata with significantly less states and these numbers are closer to a conjecture due to Gamlin. An implementation leads to explicit automata for heights 3 and 4 while up to now only the case 2 was obtained by hand. In a second approach, we consider the configurations on the twodimensional square lattice which are periodic in two directions. We suggest to place the sink ensuring that the stabilisation ends at infinity in a direction of rational slope which allows to preserve biperiodicity and a weaker form of Dhar criterion for recurrent configurations. Hence we obtain an effective algorithm defining recurrent configurations among the biperiodic and stable configurations. These biperiodic and recurrent configurations are natural candidates for being the elements of finite subgroups of the hypothetical group on configurations of the sandpile model on the square lattice. We discuss some notions allowing the definition of the law of such a group and experimentally provide some finite subgroups.

[pt] O uso da técnica bootstrap para construção de intervalos de confiança e testes de hipóteses vem aumentando consideravelmente desde seu surgimento, em 1979, devido principalmente ao rápido avanço computacional ocorrido nas últimas décadas. Neste trabalho utilizamos o bootstrap paramétrico e não-paramétrico para estudar o comportamento dos hiperparametros em modelos de espaço de estados nos casos de nível e tendência linear locais. Intervalos de confiança baseados em quatro métodos bootstrap diferentes são calculados e comparados quanto à probabilidade de cobertura, produzindo resultados satisfatórios. Constatamos também a eficiência dos testes boopstrap para os casos em que os hiperparâmetros caem no limite do espaço paramétrico, situação que inviabiliza o uso dos testes clássicos por violar uma das condições de regularidade do estimador de máxima verossimilhança. / [en] Bootstrap procedures to calculate confidence intervals and hypotheses tests had considerable growth since its first appearance, in 1979, mostly due to the rapid computational developments that occurred in the last decades. In this work we employ the parametric and nonparametric boorstrap to study the behaviour of hyperparameters in state-space models in the case of local level and linear trend. Confidence intervals based on four different bootstrap methods are computed and compared using the coverage probabilities, with satisfactory results. We also verify the efficiency of bootstrap tests in cases where the hyperparameters lie on the boundary of the parameter space, situation that makes the classical tests inadequate to use, as it violates one of the regularity conditions of the maximum likelihood estimator.

Orientador: Prof. Dr. Cristian Fabio Coletti / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2017. / Nessa dissertação estudamos a Dinâmica de Melhor Resposta de Evilsizor e Lanchier (3). Foram revisadas as demonstrações em busca de equilíbrios evolucionariamente estáveis e analisando simulações para todos os casos pertinentes. Além desta revisão, neste trabalho introduzimos o conceito de nós teimosos e os adicionamos ao modelo a fim de desestabilizar o equilíbrio no caso estudado em (3). Através das simulações, criamos a intuição de que até nos casos onde não existem equilíbrios evolucionariamente estáveis há também um equilíbrio, porém com coexistência de estratégias. Conjecturamos que esse resultado vale para o caso geral, porém conseguimos prová-lo apenas para dois casos particulares. / In this thesis we studied the Best-Response Dynamics model of Evilsizor e Lanchier (3). We reviewed proofs in search for an Evolutionary Stable Equilibrium analysing simulations for all relevant cases. Besides this revision, we introduced the concept of stubborn players and added it to the Best-Response Dynamics model hoping destabilize the Evolutionary Stable Equilibrium. Through those simulations, we conjectured that even when there is not an Evolutionary Stable Equilibrium, the model converges to another kind of equilibrium, that has coexistent strategies. We conjectured that it states for all altruistic/altruistic cases, but we only could prove it for two specific sub-cases.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Usual point and interval forecasting based on the autoregressive integrated moving average models (ARIMA) may not be suitable for modelling variables defined over the interval (0, 1). In fact, such forecasting effect predicted values outside variable domain (0, 1). The construction of the prediction intervals usually assumes (i) normality or asymptotic normality and (ii) knowledge of the parameters. If these assumptions are not fully satisfied, then the nominal coverage of the prediction intervals may not be adequate. In order to address this issue, the beta autoregressive moving average model (βARMA), which is a regarded as a suitable tool for modelling and forecasting values defined over the interval (0, 1), was considered. The goal of the present work is to propose a suit of methods for computing prediction interval linked to the βARMA model. We introduced methods for obtaining approximate prediction intervals based on (i) the normal distribution and (ii) the beta distribution quantiles. We also introduced modifications to the interval with bootstrap prediction errors (BPE) proposed for autoregressive models; and to the BCa intervals proposed for beta regression model. Moreover, based on the quantiles of the predicted values, we proposed percentiles intervals for different types of bootstrapping. The proposed prediction intervals were evaluated according to Monte Carlo simulations. Assessed results indicated that the prediction intervals based on the quantiles of the beta distribution outperformed the discussed non-bootstrapping methods. Despite some variance effects, it offered better coverage rate values. However, the BCa based prediction intervals presented well-balance results in all considered test scenarios. Therefore, the BCa prediction interval was selected as the most reliable one. Empirical evaluations of the proposed methods were applied to two actual time series: (i) the water level of the Cantareira water supply system in São Paulo from January 2003 to August 2015 and (ii) the unemployment rate data in São Paulo from January 1991 to November 2005. / O modelo beta autorregressivo de médias móveis (βARMA) foi recentemente proposto para modelagem e previsão de variáveis contínuas no intervalo (0; 1). As previsões pontuais e intervalares deste tipo de variável, por meio dos tradicionais modelos autorregressivos integrados de médias móveis (ARIMA), podem levar a valores fora do intervalo (0; 1). Ainda, a construção de intervalos de predição para valores futuros usualmente assumem (i) aproximações pela distribuição normal e (ii) parâmetros do modelo conhecidos. Quando estas suposições não são satisfeitas, a probabilidade de cobertura dos intervalos pode ficar abaixo do valor nominal. Como alternativa a este problema, intervalos de predição bootstrap tendem a apresentar coberturas mais acuradas. Neste sentido, o presente trabalho propõe diferentes intervalos de predição para o modelo βARMA. Dois desses intervalos propostos são baseados em aproximações, considerando a distribuição normal e os quantis da distribuição beta. Também são consideradas adaptações dos intervalos de predição EPB, propostos para os modelos autorregressivos, e dos intervalos BCa, propostos para o modelo de regressão beta. São também propostos intervalos percentis com diferentes reamostras bootstrap, baseados nos quantis dos valores previstos. Os intervalos de predição propostos são avaliados por meio de simulações de Monte Carlo. O intervalo baseado nos quantis da distribuição beta foi eleito como o melhor entre os intervalos sem bootstrap, uma vez que não apresentou valores de taxa de cobertura muito distorcidos em diferentes cenários. Porém, ainda apresentou variabilidade no seu comportamento. O intervalo BCa apresentou valores bons e constantes em todas as medidas avaliadas e em todos os cenários considerados. Desta forma, o intervalo BCa foi eleito como o mais confiável. Aplicações em dados dos níveis dos mananciais do sistema de captação e tratamento de água para a Grande São Paulo e das taxas de desemprego na região metropolitana de São Paulo foram consideradas como forma de avaliar empiricamente os métodos propostos.

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When a genetic factor is being studied for more than one response variable, estimates of the genetic covariances are essential, specially in breeding programs. In a genetic covariance analysis, genetic and residual mean cross-products are obtained. Stochastically, to quantify the magnitude of the joint variation of two response variables due to genetic effect with respect to the variation due to residual effect may allow one to make inferences about the significance of the associated genetic covariance. In this study it is presented tests of significance for genetic covariance upon a twofold way: tests that take into account the genetic and environmental effects and tests that only consider the genetic information. The first way refers to tests based on the mean cross-products ratio via nonparametric bootstrap resampling and Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based on adaptation of Wilks\' and Pillai\'s statistics for evaluating independence of two sets of variables. For the first type of tests, empirical distributions under the null hypothesis, i.e., null genetic covariance, were built and graphically analyzed. In addition, the exact distribution of mean cross-products ratio obtained from variables normally distributed with zero mean and finite variance was examined. Writing computational algorithms in R language to perform the proposed tests was also an objective of this study. Only under certain conditions does the probability density function of the product of two random Gaussian variables approximate a normal curve. Therefore, studying the distribution of a mean cross-products ratio as a quotient of two Gaussian variables is not suitable. Tests based on mean cross-products ratio are related to both the value of the genetic covariance and the magnitude of the latter relative to the residual covariance. And both approaches (bootstrap and simulation) are more sensitive than the tests based only on genetic information. The performance of the tests based on mean cross-products ratio is related to the quality of the original data set in terms of the MANOVA assumptions, and the test statistic does not depend on the estimation of the matrix of genetic covariances ΣG. The adaptation of Wilks\' and Pillai\'s statistics can be used to test the genetic covariance. Their approximations to a χ21 distribution were checked and the accuracy of their inferences is related to the quality of G. / Quando um fator genético está sendo estudado em mais de uma variável de resposta, estimativas das covariâncias genéticas são essenciais, especialmente para programas de melhoramento. Em uma análise de covariância genética, produtos cruzados médios devido ao efeito genético, a partir do qual é obtida a covariância genética, e devido ao efeito residual são obtidos. Estocasticamente, quantificar a magnitude da variação conjunta de duas variáveis resposta devido ao efeito genético em relação à variação devida ao efeito residual pode permitir realizar inferências sobre a covariância genética associada. Neste estudo são apresentados testes de significância para a covariância genética de duas formas: testes que levam em conta os efeitos genéticos e ambientais (ou residuais) e testes que consideram apenas a informação genética. A primeira forma refere-se testes baseados na razão de produtos cruzados médios via bootstrap não paramétrico e simulação de matrizes Wishart pelo método de Monte Carlo. A segunda maneira de testar a covariância genética refere-se a testes com base em uma adaptação das estatísticas de Wilks e Pillai para avaliar a independência de dois conjuntos de variáveis. Para o primeiro tipo de testes, as distribuições empíricas sob a hipótese nula, ou seja, covariância genética nula, foram construídas e analisadas graficamente. Além disso, foi feito um estudo analítico da distribuição da razão de produtos cruzados médios obtidos a partir de variáveis normalmente distribuídas com média zero e variância finita. Escrever algoritmos computacionais em linguagem R para realizar os testes propostos também foi um dos objetivos deste estudo. Apenas sob certas condições a função de densidade de probabilidade do produto de duas variáveis aleatórias gaussianas aproxima-se da curva normal. Por conseguinte, o estudo da distribuição da razão de produtos cruzados médios como um quociente de duas variáveis gaussianas não é adequado. Os testes baseados na razão de produtos cruzados médios estão relacionados tanto com o valor da covariância genética quanto com a magnitude desta em relação à covariância residual. Ambas as abordagens (bootstrap e simulação) mostraram-se mais sensíveis do que os testes baseados apenas nas informações genéticas. O desempenho dos testes baseados na razão de produtos cruzados médios está relacionado à qualidade dos dados originais em termos das pressuposições da MANOVA, e a estatística de teste não depende da estimação da matriz de covariâncias genéticas ΣG. A adaptação das estatísticas de Wilks e Pillai pode ser usada para testar a covariância genética. As aproximações à distribuição Χ21 foi verificada. A precisão de suas inferências está relacionada a qualidade da matriz G.

La régression Partial Least Squares (PLS), de part ses caractéristiques, est devenue une méthodologie statistique de choix pour le traitement de jeux de données issus d’études génomiques. La fiabilité de la régression PLS et de certaines de ses extensions repose, entre autres, sur une détermination robuste d’un hyperparamètre, le nombre de composantes. Une telle détermination reste un objectif important à ce jour, aucun critère existant ne pouvant être considéré comme globalement satisfaisant. Nous avons ainsi élaboré un nouveau critère de choix pour la sélection du nombre de composantes PLS basé sur la technique du bootstrap et caractérisé notamment par une forte stabilité. Nous avons ensuite pu l’adapter et l’utiliser à des fins de développement et d’amélioration de procédés de sélection de prédicteurs significatifs, ouvrant ainsi la voie à une identification rendue plus fiable et robuste des probe sets impliqués dans la caractéristique étudiée d’une pathologie. / The Partial Least Squares (PLS) regression, through its properties, has become a versatile statistic methodology for the analysis of genomic datasets.The reliability of the PLS regression and some of its extensions relies on a robust determination of a tuning parameter, the number of components. Such a determination is still a major aim since no existing criterion could be considered as a global benchmark one in the state-of-art literature. We developed a new bootstrap based stopping criterion in PLS components construction that guarantee a high level of stability. We then adapted and used it to develop and improve variable selection processes, allowing a more reliable and robust determination of significant probe sets related to the studied feature of a pathology.