The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and flexible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the flexibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests - such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data - can be easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces. / Series: Research Report Series / Department of Statistics and Mathematics

In this dissertation, three essays are presented that apply recent advances in time-series methods to the analysis of inflation and stock market index data for Taiwan. Specifically, ARCH and GARCH methodologies are used to investigate claims of increased volatility in economic time-series data since 1980. In the first essay, analysis that accounts for structural change reveals that the fundamental relationship between inflation and its variability was severed by policies implemented during economic liberalization in Taiwan in the early 1980s. Furthermore, if residuals are corrected for serial correlation, evidence in favor of ARCH effects is weakened. In the second essay, dynamic linkages between daily stock returns and daily trading volume are explored. Both linear and nonlinear dependence are evaluated using Granger causality tests and GARCH modelling. Results suggest significant unidirectional Granger causality from stock returns to trading volume. In the third essay, comparative analysis of the frequency structure of the Taiwan stock index data is conducted using daily, weekly, and monthly data. Results demonstrate that the relationship between mean return and its conditional standard deviation is positive and significant only for high-frequency daily data.

This study revolves around operators defined by conditional expectations and operators generated by random measures. Studies of operators in function spaces defined by conditional expectations first appeared in the mid 1950's by S-T.C. Moy [22] and S. Sidak [26]. N. Kalton studied them in the setting of Lp-spaces 0 < p < 1 in [15, 131 and in L1-spaces, [14], while W. Arveson [5] studied them in L2-spaces. Their averaging properties were studied by P.G. Dodds and C.B. Huijsmans and B. de Pagter in [7] and C.B. Huijsmans and B. de Pagter in [lo]. A. Lambert [17] studied their relationship with multiplication operators in C*-modules. It was shown by J.J. Grobler and B. de Pagter [8] that partial integral operators that were studied A.S. Kalitvin et a1 in [2, 4, 3, 11, 121 and the special cases of kernel operators that were, inter alia, studied by A.R. Schep in [25] were special cases of conditional expectation operators. On the other hand, operators generated by random measures or pseudo-integral operators were studied by A. Sourour [28, 271 and L.W. Weis [29,30], building on the studies of W. Arveson [5] and N. Kalton [14, 151, in the late 1970's and early 1980's. In this thesis we extend the work of J.J. Grobler and B. de Pagter [8] on Multiplication Conditional Expectation-representable (MCE-representable) operators. We also generalize the result of A. Sourour [27] and show that order continuous linear maps between ideals of almost everywhere finite measurable functions on u-finite measure spaces are MCE-representable. This fact enables us to easily deduce that sums and compositions of MCE-representable operators are again MCE-representable operators. We also show that operators generated by random measures are MCE-representable. The first chapter gathers the definitions and introduces notions and concepts that are used throughout. In particular, we introduce Riesz spaces and operators therein, Riesz and Boolean homomorphisms, conditional expectation operators, kernel and absolute T-kernel operators. In Chapter 2 we look at MCE-operators where we give a definition different from that given by J.J. Grobler and B. de Pagter in [8], but which we show to be equivalent. Chapter 3 involves random measures and operators generated by random measures. We solve the problem (positively) that was posed by A. Sourour in [28] about the relationship of the lattice properties of operators generated by random measures and the lattice properties of their generating random measures. We show that the total variation of a random signed measure representing an order bounded operator T, it being the difference of two random measures, is again a random measure and represents ITI. We also show that the set of all operators generated by a random measure is a band in the Riesz space of all order bounded operators. In Chapter 4 we investigate the relationship between operators generated by random measures and MCE-representable operators. It was shown by A. Sourour in [28, 271 that every order bounded order continuous linear operator acting between ideals of almost everywhere measurable functions is generated by a random measure, provided that the measure spaces involved are standard measure spaces. We prove an analogue of this theorem for the general case where the underlying measure spaces are a-finite. We also, in this general setting, prove that every order continuous linear operator is MCE-representable. This rather surprising result enables us to easily show that sums, products and compositions of MCE-representable operator are again MCE-representable. Key words: Riesz spaces, conditional expectations, multiplication conditional expectation-representable operators, random measures. / Thesis (Ph.D. (Mathematics))--North-West University, Potchefstroom Campus, 2004.

This study revolves around operators defined by conditional expectations and operators generated by random measures. Studies of operators in function spaces defined by conditional expectations first appeared in the mid 1950's by S-T.C. Moy [22] and S. Sidak [26]. N. Kalton studied them in the setting of Lp-spaces 0 < p < 1 in [15, 131 and in L1-spaces, [14], while W. Arveson [5] studied them in L2-spaces. Their averaging properties were studied by P.G. Dodds and C.B. Huijsmans and B. de Pagter in [7] and C.B. Huijsmans and B. de Pagter in [lo]. A. Lambert [17] studied their relationship with multiplication operators in C*-modules. It was shown by J.J. Grobler and B. de Pagter [8] that partial integral operators that were studied A.S. Kalitvin et a1 in [2, 4, 3, 11, 121 and the special cases of kernel operators that were, inter alia, studied by A.R. Schep in [25] were special cases of conditional expectation operators. On the other hand, operators generated by random measures or pseudo-integral operators were studied by A. Sourour [28, 271 and L.W. Weis [29,30], building on the studies of W. Arveson [5] and N. Kalton [14, 151, in the late 1970's and early 1980's. In this thesis we extend the work of J.J. Grobler and B. de Pagter [8] on Multiplication Conditional Expectation-representable (MCE-representable) operators. We also generalize the result of A. Sourour [27] and show that order continuous linear maps between ideals of almost everywhere finite measurable functions on u-finite measure spaces are MCE-representable. This fact enables us to easily deduce that sums and compositions of MCE-representable operators are again MCE-representable operators. We also show that operators generated by random measures are MCE-representable. The first chapter gathers the definitions and introduces notions and concepts that are used throughout. In particular, we introduce Riesz spaces and operators therein, Riesz and Boolean homomorphisms, conditional expectation operators, kernel and absolute T-kernel operators. In Chapter 2 we look at MCE-operators where we give a definition different from that given by J.J. Grobler and B. de Pagter in [8], but which we show to be equivalent. Chapter 3 involves random measures and operators generated by random measures. We solve the problem (positively) that was posed by A. Sourour in [28] about the relationship of the lattice properties of operators generated by random measures and the lattice properties of their generating random measures. We show that the total variation of a random signed measure representing an order bounded operator T, it being the difference of two random measures, is again a random measure and represents ITI. We also show that the set of all operators generated by a random measure is a band in the Riesz space of all order bounded operators. In Chapter 4 we investigate the relationship between operators generated by random measures and MCE-representable operators. It was shown by A. Sourour in [28, 271 that every order bounded order continuous linear operator acting between ideals of almost everywhere measurable functions is generated by a random measure, provided that the measure spaces involved are standard measure spaces. We prove an analogue of this theorem for the general case where the underlying measure spaces are a-finite. We also, in this general setting, prove that every order continuous linear operator is MCE-representable. This rather surprising result enables us to easily show that sums, products and compositions of MCE-representable operator are again MCE-representable. Key words: Riesz spaces, conditional expectations, multiplication conditional expectation-representable operators, random measures. / Thesis (Ph.D. (Mathematics))--North-West University, Potchefstroom Campus, 2004.

In this dissertation, three essays are presented that apply recent advances in time-series methods to the analysis of inflation and stock market index data for Taiwan. Specifically, ARCH and GARCH methodologies are used to investigate claims of increased volatility in economic time-series data since 1980. In the first essay, analysis that accounts for structural change reveals that the fundamental relationship between inflation and its variability was severed by policies implemented during economic liberalization in Taiwan in the early 1980s. Furthermore, if residuals are corrected for serial correlation, evidence in favor of ARCH effects is weakened. In the second essay, dynamic linkages between daily stock returns and daily trading volume are explored. Both linear and nonlinear dependence are evaluated using Granger causality tests and GARCH modelling. Results suggest significant unidirectional Granger causality from stock returns to trading volume. In the third essay, comparative analysis of the frequency structure of the Taiwan stock index data is conducted using daily, weekly, and monthly data. Results demonstrate that the relationship between mean return and its conditional standard deviation is positive and significant only for high-frequency daily data.

Cette thèse peut être divisée en trois parties.Dans la première partie, nous étudions des méthodes d'adaptation au niveau de bruit dans le modèle de régression linéaire en grande dimension. Nous prouvons que deux estimateurs à racine carrée, peuvent atteindre les vitesses minimax d'estimation et de prédiction. Nous montrons qu'une version similaire construite à parti de médianes de moyenne, peut encore atteindre les mêmes vitesses optimales en plus d'être robuste vis-à-vis de l'éventuelle présence de données aberrantes.La seconde partie est consacrée à l'analyse de plusieurs modèles de dépendance conditionnelle. Nous proposons plusieurs tests de l'hypothèse simplificatrice qu'une copule conditionnelle est constante vis-à-vis de son évènement conditionnant, et nous prouvons la consistance d'une technique de ré-échantillonage semi-paramétrique. Si la copule conditionnelle n'est pas constante par rapport à sa variable conditionnante, alors elle peut être modélisée via son tau de Kendall conditionnel. Nous étudions donc l'estimation de ce paramètre de dépendance conditionnelle sous 3 approches différentes : les techniques à noyaux, les modèles de type régression et les algorithmes de classification.La dernière partie regroupe deux contributions dans le domaine de l'inférence.Nous comparons et proposons différents estimateurs de fonctionnelles conditionnelles régulières en utilisant des U-statistiques. Finalement, nous étudions la construction et les propriétés théoriques d'intervalles de confiance pour des ratios de moyenne sous différents choix d'hypothèses et de paradigmes. / This thesis can be divided into three parts.In the first part, we study adaptivity to the noise level in the high-dimensional linear regression framework. We prove that two square-root estimators attains the minimax rates of estimation and prediction. We show that a corresponding median-of-means version can still attains the same optimal rates while being robust to outliers in the data.The second part is devoted to the analysis of several conditional dependence models.We propose some tests of the simplifying assumption that a conditional copula is constant with respect to its conditioning event, and prove the consistency of a semiparametric bootstrap scheme.If the conditional copula is not constant with respect to the conditional event, then it can be modelled using the corresponding Kendall's tau.We study the estimation of this conditional dependence parameter using 3 different approaches : kernel techniques, regression-type models and classification algorithms.The last part regroups two different topics in inference.We review and propose estimators for regular conditional functionals using U-statistics.Finally, we study the construction and the theoretical properties of confidence intervals for ratios of means under different sets of assumptions and paradigms.

Diese Arbeit befasst sich mit der Entwicklung einer Theorie bedingter Mengen. Bedingte Mengenlehre ist reich genug um einen bedingten mathematischen Diskurs zu führen, dessen Möglichkeit wir durch die Konstruktion einer bedingten Topologielehre und bedingter reeller Analysis aufzeigen. Wir beweisen die bedingte Version folgender Sätze: Ultrafilterlemma, Tychonoff, Borel-Lebesgue, Heine-Borel, Bolzano-Weierstraß, und das Gaplemma von Debreu. Darüberhinaus beweisen wir die bedingte Version derjenigen Resultate der klassischen Mathematik, die in den Beweisen dieser Sätze benötigt werden, beginnend mit der Mengenlehre. Wir diskutieren die Verbindung von bedingter Mengenlehre zur Garben-, Topos- und L0-Theorie. / In this thesis, we develop a theory of conditional sets. Conditional set theory is sufficiently rich in order to allow for a conditional mathematical reasoning, the possibility of which we demonstrate by constructing a conditional general topology and a conditional real analysis. We prove the conditional version of the following theorems: Ultrafilter Lemma, Tychonoff, Borel-Lebesgue, Heine-Borel, Bolzano-Weierstraß, and Debreu’s Gap Lemma. Moreover, we prove the conditional version of those results in classical mathematics which are needed in the proofs of these theorems, starting from set theory. We discuss the connection of conditional set theory to sheaf, topos and L0-theory.

A tese da equivalência afirma que as condicionais indicativas e a condicional material possuem condições de verdade equivalentes, i.e., elas são falsas quando possuem a antecedente verdadeira e a consequente falsa, mas são verdadeiras nas demais circunstâncias. Essa tese tem algumas consequências contra-intuitivas. Por exemplo, ela implica que qualquer condicional com uma antecedente falsa é verdadeira. Isso é estranho, pois não é intuitivo pensar que a condicional “Se a lua é feita de queijo, então 2 +2 = 4” é verdadeira somente porque a lua não é feita de queijo. Antes, pensamos que a constituição da lua não tem qualquer relação com as verdades da aritmética. Essa perplexidade é um dos paradoxos da condicional material. No primeiro e segundo capítulos apresento as duas tentativas mais influentes de defender a tese da equivalência face aos paradoxos, as propostas de Paul Grice e Frank Jackson. Argumento que elas são incapazes de eliminar os paradoxos, pois tentam explicar a sua origem em práticas linguísticas. No terceiro capítulo eu argumento que a real causa dos aspectos paradoxais da condicional material são intuições epistêmicas e metafísicas que devem ser recusadas, pois resultam de erros de raciocínio. / The equivalence thesis states that indicative conditionals and the material conditional have the same truth conditions i.e., they are false when they have a truth antecedent and a false consequent, but true in any other circumstances. This thesis has some counterintuitive consequences. For instance, it implies that any conditional with a false antecedent is true. This is odd, for it is not intuitive to think that the conditional “If the moon is made of cheese, then 2 + 2 = 4” is true solely in virtue of the moon not being made of cheese. We would rather think that the moon’s composition and arithmetic truths aren’t related to each other. This perplexity is one of the paradoxes of the material conditional. In the first and second chapters, I present the two most influential attempts of defending the equivalence thesis from the paradoxes: the proposals of Paul Grice and Frank Jackson. I argue that the attempts are nonetheless unable of dismissing the paradoxes, because they attempt to explain their origins as stemming from linguistic practices. In the third chapter, I argue that the real cause of the paradoxical aspects of the material conditional are epistemic and metaphysical intuitions that must be refused, for they result from flawed reasoning.

A tese da equivalência afirma que as condicionais indicativas e a condicional material possuem condições de verdade equivalentes, i.e., elas são falsas quando possuem a antecedente verdadeira e a consequente falsa, mas são verdadeiras nas demais circunstâncias. Essa tese tem algumas consequências contra-intuitivas. Por exemplo, ela implica que qualquer condicional com uma antecedente falsa é verdadeira. Isso é estranho, pois não é intuitivo pensar que a condicional “Se a lua é feita de queijo, então 2 +2 = 4” é verdadeira somente porque a lua não é feita de queijo. Antes, pensamos que a constituição da lua não tem qualquer relação com as verdades da aritmética. Essa perplexidade é um dos paradoxos da condicional material. No primeiro e segundo capítulos apresento as duas tentativas mais influentes de defender a tese da equivalência face aos paradoxos, as propostas de Paul Grice e Frank Jackson. Argumento que elas são incapazes de eliminar os paradoxos, pois tentam explicar a sua origem em práticas linguísticas. No terceiro capítulo eu argumento que a real causa dos aspectos paradoxais da condicional material são intuições epistêmicas e metafísicas que devem ser recusadas, pois resultam de erros de raciocínio. / The equivalence thesis states that indicative conditionals and the material conditional have the same truth conditions i.e., they are false when they have a truth antecedent and a false consequent, but true in any other circumstances. This thesis has some counterintuitive consequences. For instance, it implies that any conditional with a false antecedent is true. This is odd, for it is not intuitive to think that the conditional “If the moon is made of cheese, then 2 + 2 = 4” is true solely in virtue of the moon not being made of cheese. We would rather think that the moon’s composition and arithmetic truths aren’t related to each other. This perplexity is one of the paradoxes of the material conditional. In the first and second chapters, I present the two most influential attempts of defending the equivalence thesis from the paradoxes: the proposals of Paul Grice and Frank Jackson. I argue that the attempts are nonetheless unable of dismissing the paradoxes, because they attempt to explain their origins as stemming from linguistic practices. In the third chapter, I argue that the real cause of the paradoxical aspects of the material conditional are epistemic and metaphysical intuitions that must be refused, for they result from flawed reasoning.

A tese da equivalência afirma que as condicionais indicativas e a condicional material possuem condições de verdade equivalentes, i.e., elas são falsas quando possuem a antecedente verdadeira e a consequente falsa, mas são verdadeiras nas demais circunstâncias. Essa tese tem algumas consequências contra-intuitivas. Por exemplo, ela implica que qualquer condicional com uma antecedente falsa é verdadeira. Isso é estranho, pois não é intuitivo pensar que a condicional “Se a lua é feita de queijo, então 2 +2 = 4” é verdadeira somente porque a lua não é feita de queijo. Antes, pensamos que a constituição da lua não tem qualquer relação com as verdades da aritmética. Essa perplexidade é um dos paradoxos da condicional material. No primeiro e segundo capítulos apresento as duas tentativas mais influentes de defender a tese da equivalência face aos paradoxos, as propostas de Paul Grice e Frank Jackson. Argumento que elas são incapazes de eliminar os paradoxos, pois tentam explicar a sua origem em práticas linguísticas. No terceiro capítulo eu argumento que a real causa dos aspectos paradoxais da condicional material são intuições epistêmicas e metafísicas que devem ser recusadas, pois resultam de erros de raciocínio. / The equivalence thesis states that indicative conditionals and the material conditional have the same truth conditions i.e., they are false when they have a truth antecedent and a false consequent, but true in any other circumstances. This thesis has some counterintuitive consequences. For instance, it implies that any conditional with a false antecedent is true. This is odd, for it is not intuitive to think that the conditional “If the moon is made of cheese, then 2 + 2 = 4” is true solely in virtue of the moon not being made of cheese. We would rather think that the moon’s composition and arithmetic truths aren’t related to each other. This perplexity is one of the paradoxes of the material conditional. In the first and second chapters, I present the two most influential attempts of defending the equivalence thesis from the paradoxes: the proposals of Paul Grice and Frank Jackson. I argue that the attempts are nonetheless unable of dismissing the paradoxes, because they attempt to explain their origins as stemming from linguistic practices. In the third chapter, I argue that the real cause of the paradoxical aspects of the material conditional are epistemic and metaphysical intuitions that must be refused, for they result from flawed reasoning.