The main objective of this thesis is the development of a nonparametric sequential estimation technique for the off-pulse interval(s) of a source function originating from a pulsar. It is important to identify the off-pulse interval of each pulsar accurately, since the properties of the off-pulse emissions are further researched by astrophysicists in an attempt to detect potential emissions from the associated pulsar wind nebula (PWN). The identification technique currently used in the literature is subjective in nature, since it is based on the visual inspection of the histogram estimate of the pulsar light curve. The developed nonparametric estimation technique is not only objective in nature, but also accurate in the estimation of the off-pulse interval of a pulsar, as evident from the simulation study and the application of the developed technique to observed pulsar data. The first two chapters of this thesis are devoted to a literature study that provides background information on the pulsar environment and -ray astronomy, together with an explanation of the on-pulse and off-pulse interval of a pulsar and the importance thereof for the present study. This is followed by a discussion on some fundamental circular statistical ideas, as well as an overview of kernel density estimation techniques. These two statistical topics are then united in order to illustrate kernel density estimation techniques applied to circular data, since this concept is the starting point of the developed nonparametric sequential estimation technique. Once the basic theoretical background of the pulsar environment and circular kernel density estimation has been established, the new sequential off-pulse interval estimator is formulated. The estimation technique will be referred to as `SOPIE'. A number of tuning parameters form part of SOPIE, and therefore the performed simulation study not only serves as an evaluation of the performance of SOPIE, but also as a mechanism to establish which tuning parameter configurations consistently perform better than some other configurations. In conclusion, the optimal parameter configurations are utilised in the application of SOPIE to pulsar data. For several pulsars, the sequential off-pulse interval estimators are compared to the off-pulse intervals published in research papers, which were identified with the subjective \eye-ball" technique. It is found that the sequential off-pulse interval estimators are closely related to the off-pulse intervals identified with subjective visual inspection, with the benefit that the estimated intervals are objectively obtained with a nonparametric estimation technique. / PhD (Statistics), North-West University, Potchefstroom Campus, 2014

The main objective of this thesis is the development of a nonparametric sequential estimation technique for the off-pulse interval(s) of a source function originating from a pulsar. It is important to identify the off-pulse interval of each pulsar accurately, since the properties of the off-pulse emissions are further researched by astrophysicists in an attempt to detect potential emissions from the associated pulsar wind nebula (PWN). The identification technique currently used in the literature is subjective in nature, since it is based on the visual inspection of the histogram estimate of the pulsar light curve. The developed nonparametric estimation technique is not only objective in nature, but also accurate in the estimation of the off-pulse interval of a pulsar, as evident from the simulation study and the application of the developed technique to observed pulsar data. The first two chapters of this thesis are devoted to a literature study that provides background information on the pulsar environment and -ray astronomy, together with an explanation of the on-pulse and off-pulse interval of a pulsar and the importance thereof for the present study. This is followed by a discussion on some fundamental circular statistical ideas, as well as an overview of kernel density estimation techniques. These two statistical topics are then united in order to illustrate kernel density estimation techniques applied to circular data, since this concept is the starting point of the developed nonparametric sequential estimation technique. Once the basic theoretical background of the pulsar environment and circular kernel density estimation has been established, the new sequential off-pulse interval estimator is formulated. The estimation technique will be referred to as `SOPIE'. A number of tuning parameters form part of SOPIE, and therefore the performed simulation study not only serves as an evaluation of the performance of SOPIE, but also as a mechanism to establish which tuning parameter configurations consistently perform better than some other configurations. In conclusion, the optimal parameter configurations are utilised in the application of SOPIE to pulsar data. For several pulsars, the sequential off-pulse interval estimators are compared to the off-pulse intervals published in research papers, which were identified with the subjective \eye-ball" technique. It is found that the sequential off-pulse interval estimators are closely related to the off-pulse intervals identified with subjective visual inspection, with the benefit that the estimated intervals are objectively obtained with a nonparametric estimation technique. / PhD (Statistics), North-West University, Potchefstroom Campus, 2014

This thesis is mainly concerned with the estimation of conditional probabilities in two-way contingency tables, that is probabilities of type P(R=i,S=j|X=x), for (i,j) in {1, . . . , r}×{1, . . . , s}, where R and S are the two categorical variables forming the contingency table, with r and s levels respectively, and X is a vector of explanatory variables possibly associated with R, S, or both. Analyzing such a conditional distribution is often of interest, as this allows to go further than the usual unconditional study of the behavior of the variables R and S. First, one can check an eventual effect of these covariates on the distribution of the individuals through the cells of the table, and second, one can carry out usual analyses of contingency tables, such as independence tests, taking into account, and removing in some sense, this effect. This helps for instance to identify the external factors which could be responsible for an eventual association between R and S. This also gives the possibility to adapt for a possible heterogeneity in the population of interest, when analyzing the table.

在過去研究犯罪經濟學的理論文獻上，失業率對各犯罪類型的影響為正向關係，但在實証文獻上的研究發現，卻有愈來愈多的証據支持此二個變數間的負向或無關係。為了解釋上述正向與負向間相反的矛盾關係，本篇論文嘗試利用兩種模型(非參數與非參數模型)與兩種效果(機會效果與動機效果)來解釋此二變數間的關係，此亦是本論文主要貢獻。其中機會效果是用以解釋失業率與犯罪間的負向關係，動機效果則用以解釋正向關係。在非參數模型中，利用失業率為景氣循環的代理變數，發現失業率與竊盜間存在正向關係，此與大多實証研究相符；失業率則和妨害風化與殺人犯罪間呈現負向相關；失業率與傷害罪間則沒有明顯正負關係。研究亦顯示，不同的犯罪類型在不同的參數模型下，統計的顯著性亦有不同，而在不同年齡層(青少年與成年人)的犯罪模型則更與理論模型結論相符。 / According to the theoretical literature on criminal economics, unemployment rate tends to be positively correlated to all types of crimes. However, more and more empirical evidence suggests otherwise. In order to clarify the relationship, this study exploits both nonparametric and parametric models and considers two effects, including opportunity and motivation effects. The presence of the opportunity effect leads to be a negative correlation between unemployment rate and crimes, while the presence of the motivation effect gives a positive correlation. Under nonparametric model where unemployment rate is used as a proxy for business cycles, we only found that there is positive correlation between unemployment rate and robbery, while obscenity and homicide are found to be negatively correlated with unemployment rate. This is in line with most empirical studies. Little correlation evidence is found for unemployment and other types of crimes. Under parametric model, the study indicates that the statistical significance differs in models, and depends on crime variable used. We found more consistent results with theoretic models for the age groups (teenagers and adults).

À partir des observations Z(n) = {(Xi, Yi), i = 1, ..., n} satisfaisant Yi = f(Xi) + ζi, nous voulons reconstruire la fonction f. Nous évaluons la qualité d'estimation par deux critères : le risque Ls et le risque uniforme. Dans ces deux cas, les hypothèses imposées sur la distribution du bruit ζi serons de moment borné et de type sous-gaussien respectivement. En proposant une collection des estimateurs à noyau, nous construisons une procédure, qui est initié par Goldenshluger et Lepski, pour choisir l'estimateur dans cette collection, sans aucune condition sur f. Nous prouvons ensuite que cet estimateur satisfait une inégalité d'oracle, qui nous permet d'obtenir les estimations minimax et minimax adaptatives sur les classes de Hölder anisotropes. / From the observation Z(n) = {(Xi, Yi), i = 1, ..., n} satisfying Yi = f(Xi) + ζi, we would like to approximate the function f. This problem will be considered in two cases of loss function, Ls-risk and uniform risk, where the condition imposed on the distribution of the noise ζi is of bounded moment and of type sub-gaussian, respectively. From a proposed family of kernel estimators, we construct a procedure, which is initialized by Goldenshluger and Lepski, to choose in this family a final estimator, with no any assumption imposed on f. Then, we show that this estimator satisfies an oracle inequality which implies the minimax and minimax adaptive estimation over the anisotropic Hölder classes.

We propose Bayesian methods for selecting and estimating different types of mixture models which are widely used inGenetics and MolecularBiology. We specifically propose data-driven selection and estimation methods for a generalized mixture model, which accommodates the usual (independent) and the first-order (dependent) models in one framework, and QTL (quantitativetrait locus) mapping models for independent and pedigree data. For clustering genes through a mixture model, we propose three nonparametric Bayesian methods: a marginal nested Dirichlet process (NDP), which is able to cluster distributions and, a predictive recursion clustering scheme (PRC) and a subset nonparametric Bayesian (SNOB) clustering algorithm for clustering bigdata. We analyze and compare the performance of the proposed methods and traditional procedures of selection, estimation and clustering in simulated and real datasets. The proposed methods are more flexible, improve the convergence of the algorithms and provide more accurate estimates in many situations. In addition, we propose methods for estimating non observable QTLs genotypes and missing parents and improve the Mendelian probability of inheritance of nonfounder genotype using conditional independence structures.We also suggest applying diagnostic measures to check the goodness of fit of QTLmappingmodels. / Nos propomos métodos Bayesianos para selecionar e estimar diferentes tipos de modelos de mistura que são amplamente utilizados em Genética e Biologia Molecular. Especificamente, propomos métodos direcionados pelos dados para selecionar e estimar um modelo de mistura generalizado, que descreve o modelo de mistura usual (independente) e o de primeira ordem numa mesma estrutura, e modelos de mapeamento de QTL com dados independentes e familiares. Para agrupar genes através de modelos de mistura, nos propomos três métodos Bayesianos não-paramétricos: o processo de Dirichlet aninhado que possibilita agrupamento de distribuições e, um algoritmo preditivo recursivo e outro Bayesiano não- paramétrico exato para agrupar dados de alta dimensão. Analisamos e comparamos o desempenho dos métodos propostos e dos procedimentos tradicionais de seleção e estimação de modelos e agrupamento de dados em conjuntos de dados simulados e reais. Os métodos propostos são mais flexíveis, aprimoram a convergência dos algoritmos e apresentam estimativas mais precisas em muitas situações. Além disso, nos propomos procedimentos para estimar o genótipo não observável dos QTL se de pais faltantes e melhorar a probabilidade Mendeliana de herança genética do genótipo dos descendentes através da estrutura condicional de independência entre as variáveis. Também sugerimos aplicar medidas de diagnóstico para verificar a qualidade do ajuste dos modelos de mapeamento de QTLs.

Cette thèse cherche à approfondir la nature et la forme des relations entre les inégalités éducatives et le développement. Elle s’inscrit dans le prolongement des analyses engagées sur les liens éducation/croissance et inégalités/croissance, en essayant d’apporter un éclairage complémentaire sur ces deux relations. Elle vise à retracer de manière stylisée l’évolution des inégalités éducatives particulièrement dans les pays en développement et à caractériser la non-linéarité de la relation à partir de l’estimation de modèles non-paramétriques et semi-paramétriques. Cette thèse est constituée de trois chapitres auxquels correspondent des objectifs, des bases de données et des méthodologies spécifiques. Dans un premier chapitre, nous proposons une nouvelle base mondiale sur les inégalités d’éducation. La majorité des travaux sur la relation entre capital humain et développement économique ont principalement appréhendé la mesure du capital humain à travers des mesures de l’éducation en utilisant notamment la moyenne d’années de scolarisation (stock du capital humain). Notre base de données, qui présente une mesure alternative du capital humain, tend à améliorer sensiblement le mode de calcul des inégalités de l’éducation. Elle exploite toute la richesse des données désagrégées, corrige les pondérations inappropriées et affine certaines hypothèses réductrices sur les durées des cycles d’enseignement et les niveaux d’éducation retenus. Nous avons aussi généralisé la formule proposée par Berthélemy (2006) sur l’indice de Gini de l’éducation. Le domaine de variation possible de cet indice est identifié graphiquement selon la moyenne d’années de scolarisation et les durées cumulées des cycles d’enseignement. Nous mettons en évidence, dans le cadre du chapitre II, l’existence d’une relation non linéaire entre les inégalités dans l’éducation et le développement économique en utilisant des modèles non-paramétriques et semi-paramétriques qui n’exigent pas de formes fonctionnelles prédéfinies à l’avance. Plusieurs phases sont ainsi mises en évidence : les trois premières sont repérées seulement par rapport aux niveaux de développement ; deux autres sont identifiées à la fois par des seuils de développement et d’inégalité d’éducation ; une sixième et dernière phase est définie par rapport au seul niveau d’inégalité d’éducation. Nous montrons que c’est dans la troisième et cinquième phases que la réduction de l’inégalité d’éducation présente l’impact le plus bénéfique sur le développement économique.Au-delà du schéma général mis en évidence sur le plan transnational dans les chapitres I et II, nous explorons dans le chapitre III la nature de cette relation au plan régional dans le cas du Maroc, pour lequel nous disposons de données aux niveaux communal et provincial. La non-linéarité de la relation est aussi confirmée. La troisième phase repérée au chapitre II est subdivisée, dans le cas des provinces marocaines, en deux sous phases qui présentent un impact différencié selon un seuil de développement et d’inégalité d’éducation. / This thesis seeks to deepen the nature and the shape of the relationships between educational inequalities and development. It goes along with the prolongation of the analyses undertaken about the relationships between both education & growth; and inequality & growth, by trying to shed additional light on these two. It aims to retrace, in a schematic way, the evolution of educational inequalities particularly in the developing countries; and also to characterize the nonlinearity of this link using nonparametric and semiparametric estimation models.This thesis consists of three chapters that correspond to specific objectives, databases and methodologies. In the first chapter, we propose a new dataset on the inequalities of education. Most of the studies on the relationship between human capital and economic development have mainly apprehended the measurement of human capital through quantitative education indicators, using namely the average of years of schooling (human capital stock). Our database, which presents an alternative measure of human capital, tends to improve significantly the way in which inequalities in education are calculated. It employs all the abundance of disaggregated data, corrects inappropriate weightings and refines some reductive assumptions about the durations of schooling cycles and the levels of education. We have also generalized the formula proposed by Berthélemy (2006) on the Gini index of education. The possible variation range of this index is graphically identified according to the average years of schooling and the cumulative duration of the schooling cycles. In Chapter II, we reveal the existence of a nonlinear relationship between inequalities in education and economic development using nonparametric and semiparametric models that do not require predefined functional forms. Several phases are therefore highlighted: the first three are identified only according to the level of development; then two other phases are recognized by combining thresholds of both development and education inequality; the sixth and final phase is defined by the educational inequality level alone. We show that the phases during which the reduction of educational inequality presents the most beneficial impact on economic development are the third and the fifth.Beyond the general outline highlighted at the transnational level in Chapters I and II, we explore in Chapter III the nature of this relationship at the regional level in the case of Morocco, for which we have data at both the municipal and provincial levels. We also confirm the nonlinearity of the relationship. The third phase, identified in Chapter II, is divided to two sub-phases in the case of the Moroccan provinces which have a differentiated impact according to a threshold of development and inequality of education.

Uma proporção significativa dos alunos dos cursos de graduação em Geografia do IGDEMA/UFAL apresenta dificuldades na aprendizagem de Cartografia, particularmente de escala cartográfica linear. Pouquíssimos trabalhos apresentaram situações similares em outras universidades do Brasil e propuseram alternativas mitigadoras, embora com ênfase no curso de licenciatura. Nesse contexto, o presente trabalho tomou como objetivo desenvolver um procedimento de otimização da aprendizagem de escala cartográfica linear por meio da conscientização e motivação prévias discentes e contrapartidas bilaterais na aplicação de um processo de ensino-aprendizagem junto aos alunos do segundo período de graduação em Geografia do IGDEMA/UFAL em 2013/2. As bases teóricas adotadas para tal foram um conceito da psicologia pedagógica processo educativo trilateral , dois conceitos da teoria socioconstrutivista internalização das funções psicológicas superiores e zona de desenvolvimento proximal e a teoria da andragogia. Coerente com o objetivo e com respaldos das bases teóricas, foi aplicado o método de aula expositiva adaptado à implementação do processo pedagógico. Este processo envolveu a fase de avaliação prévia (exposição e prática preparatórias e posterior diálogo) e a fase de avaliação definitiva (exposições e práticas mais concentradas). Por ser preponderante, a avaliação definitiva precisou atender às exigências de planejamento e procedimentos administrativos, a fim de se minimizar a relativa falta de fidedignidade de seus escores para, em seguida, submeter-se a duas etapas obrigatórias do processo da sua validação. A primeira, que foi a verificação do requisito da validade, se deu por processo qualitativo em prol da representatividade de seu conteúdo mediante o universo Escala Cartográfica e dessa aprendizagem; e a segunda etapa, verificação do requisito da fidedignidade, processou-se pela análise estatística de consistência interna entre seus quesitos. Como a avaliação definitiva atendeu a esses requisitos de validação, as suas medidas de aprendizagem se tornaram confiáveis para os testes de diferenças aplicados conjuntamente com as medidas de aprendizagem similares da avaliação prévia. Assim, obteve-se o nível de êxito do processo pedagógico aplicado. Como resultado, a comparação dos dados das duas avaliações não indicou evolução esperada das notas de cada aluno. Então como causas desse resultado, em função da parte expressiva dos alunos, podem ser citadas: o processo aplicado se revelou ambicioso, a prática de variados exercícios mesmo com auxílio de demonstrações de cálculos revelou-se um desafio e modificações de escala cartográfica se revelaram problemática. Dessa forma, a conclusão é que esse processo de ensino-aprendizagem precisa ser revisto em parte, ou seja, revelam-se necessários procedimentos pedagógicos para esses estudantes ainda dependentes em virtude de fatores limitantes, particularmente a base matemática ineficiente. / A significant proportion of the undergraduates in the geography courses of the IGDEMA/UFAL present learning difficulties, particularly in relation to liner cartographic scale. Very few papers have identified similar situations in other universities in Brazil and have proposed mitigation alternatives, although with an emphasis on teaching degree courses. In this context, this work aimed at developing a learning procedure in order to optimize the learning of linear cartographic scale through awareness development and previous student motivation, as well as through bilateral counterparts in implementing a teaching/learning process focused on the se undergraduates of the second term in the first year of studies in Geography course of the IGDEMA/UFAL program, in 2013/2. The theoretical framework of the study included one concept of the pedagogical psychology trilateral educational process , two concepts of the social constructivist theory internalization of higher psychological functions, and proximal development zone as well as the andragogy theory. In order to be coherent with the study objective and the adopted theoretical framework, the expositive teaching method was used, although adapted to the target pedagogical process. This process involved a prior evaluation phase (presentation and preparatory practices and subsequent dialogue) and the phase of final assessment (presentations and more focused practices). Because it is preponderant, the definitive assessment had to meet planning requirements and administrative procedures, in order to minimize the relative unreliability of the scores, so that it could undergo the two mandatory steps of the process of validation. The first step verification of the validity requirement was implemented through a qualitative process, observing the representativeness of its content, based upon the Cartographic Scale universe and related learning; and the second step, verification of the reliability requirement, was developed through statistical analysis for the internal consistency of the adopted questions. As the final evaluation met these validation requirements, their learning measures were considered to be reliable for testing differences, applied within the similar learning measures of the prior assessment. As a result, the comparative data of both evaluations did not indicate the expected evolution in the students grades. Then, as those results reasons, considering the biggest amount of the students, we may cite: the applied process was too much ambitious, the practice of varied exercises though with calculation demonstrations, could be considered a challenge, and cartographic scale changes seemed to cause problems to them. Hence, the conclusion is that this teaching/learning process needs to be revised in part, which means, pedagogical proceeds might be necessary for those still dependent students, considering these limitation factors, particularly the insufficient mathematics basis.

A literatura científica vem debatendo sobre a existência de uma associação entre diabetes mellitus (DM) e demência, doença de Alzheimer (DA) e demência vascular (DV). O DM é um conhecido fator de risco para a doença cerebrovascular (DCV) e DV, porém não há consenso até o momento do real papel do DM no desenvolvimento das alterações neuropatológicas da DA. Objetivos: verificar a associação entre DM e demência, DM e alterações neuropatológicas da DA e DV. Métodos: os dados foram coletados do Banco de Encéfalos Humanos do Grupo de Estudos em Envelhecimento Cerebral da FMUSP estudados de 2004 a 2015. A amostra foi dividida em dois grupos: não diabéticos e diabéticos. Os diagnósticos de DM e de demência foram estabelecidos post-mortem mediante entrevista com informante. O diagnóstico de demência exigiu escore >= 1 na Escala de Avaliação Clínica da Demência (CDR) e Questionário sobre Declínio Cognitivo no Idoso (IQCODE) >= 3,42. O diagnóstico etiológico da demência foi determinado por exame neuropatológico por imuno-histoquímica. A proporção de casos de demência, de DA e de DV de não diabéticos e diabéticos foi determinada, assim como a relação entre DM e placas neuríticas (PN) e emaranhados neurofibrilares (ENF), e neuropatologia vascular. As análises estatísticas empregadas foram o teste de Mann-Whitney e regressão linear múltipla para variáveis quantitativas, teste de ?2, teste exato de Fisher e regressão logística múltipla para variáveis categóricas. Resultados: amostra total foi de 1.037 indivíduos, sendo 758 não diabéticos (73,1%) e 279 diabéticos (26,9%). Demência foi constatada em 28,7% em diabéticos. O DM não se associou à frequência mais elevada de demência (OR: 1,22; IC 95%: 0,81-1,82; p=0,34). O DM não está associado com ENF (p=0,81), PN (p=0,31), grupo infarto (p=0,94), angiopatia amiloide (p=0,42) e arteriolosclerose hialina (p=0,07). Após o ajuste para variáveis demográficas e para os fatores de risco vascular, o diagnóstico de DM não se associou ao diagnóstico neuropatológico de DA e vascular. Conclusão: o DM não está associado à demência e às alterações neuropatológicas da DA e de DV / The scientific literature has been debating the existence of an association between diabetes mellitus (DM) and dementia, Alzheimer\'s disease (AD) and vascular dementia (VaD). DM is a known risk factor for cerebrovascular disease (CVD) and VaD, but there is still no consensus on the real role of DM in the development of AD neuropathology. Objectives: to investigate the association among DM and dementia, neuropathology (NP) of AD and VaD. Methods: Data were collected from the cases included in the Brain Bank of the Brazilian Aging Brain Study Group between 2004 and 2015. Cases were divided into 2 groups: no diabetics and diabetics. Clinical diagnosis of dementia was determined by the scores >= 1.0 in the Clinical Dementia Rating (CDR) and >= 3.42 in the Informant Questionnaire on Cognitive Decline in the Elderly (IQCODE). Etiological diagnoses of dementia were determined by neuropathological examination, using immunohistochemistry. The proportion of dementia cases, AD and VaD of no diabetics and diabetics were investigated as well as the relationship among DM and neuritic plaques (NPq) and neurofibrillary tangles (NFT). Mann-Whitney test and multiple linear regression for quantitative variables, and chi-square test and multiple logistic regression for categorical variables were the statistical analyses applied. Results: Total sample included 1037 subjects, divided in 758 (73.1%) no diabetics and 279 diabetics (26.9%). Dementia was present in 27.8% of diabetics. DM did not increase the frequency for dementia (OR: 1.22; IC 95%: 0.81-1.82; p=0.34). DM was not associated with NFT (p=0.81), NPq (p=0.31), infarct group (0.94), cerebral amyloid angiopathy (0.42) and hyaline arteriolosclerosis (p=0.07). After adjustment for demographic variables and vascular risk factors, DM was not associated with DA and vascular NP. Conclusion: DM is not associated with dementia, AD and vascular neuropathology

Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Minimax-Sinn aufweisen kann. Für zeit-diskrete Beobachtungen von maximalem Abstand Delta konvergiert die Galerkin-Schätzung immer noch mit obiger Rate, sofern Delta is in etwa von der Ordnung T^(-1/2). Hingegen wird bewiesen, dass für festes Delta unabhängig von T die Rate sich signifikant verschlechtern muss, indem eine untere Schranke von T^(-s/(2s+6)) gezeigt wird. Außerdem wird eine adaptive Schätzung basierend auf Wavelet-Thresholding-Techniken für das assoziierte schlechtgestellte Problem konstruiert. Diese nichtlineare Schätzung erreicht die obige Minimax-Rate sogar für die allgemeinere Klasse der Besovräume B^s_(p,infinity) mit p>max(6/(2s+3),1). Die Restriktion p>=max(6/(2s+3),1) muss für jede Schätzung gelten und ist damit inhärent mit dem Schätzproblem verknüpft. Schließlich wird ein Hypothesentest mit nichtparametrischer Alternative vorgestellt, der zum Beispiel für das Testen auf Gedächtnis verwendet werden kann. Dieser Test ist anwendbar für eine L^2-Trennungsrate zwischen Hypothese und Alternative der Ordnung T^(-s/(2s+2.5)). Diese Rate ist wiederum beweisbar optimal für jede mögliche Teststatistik. Für die Beweise müssen die Parameterabhängigkeit der stationären Lösungen sowie die Abbildungseigenschaften der assoziierten Kovarianzoperatoren detailliert bestimmt werden. Weitere Resultate von allgemeinem Interessen beziehen sich auf die Mischungseigenschaft der stationären Lösung, eine Fallstudie zu exponentiellen Gewichtsfunktionen sowie der Approximation des stationären Prozesses durch autoregressive Prozesse in diskreter Zeit. / Let (X(t), t>= -r) be a stationary stochastic process solving the affine stochastic delay differential equation dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, with sigma>0, (W(t), t>=0) a standard one-dimensional Brownian motion and with a continuous linear functional L on the space of continuous functions on [-r,0], represented by a finite signed measure a. Assume that a trajectory (X(t), -r 0. This rate is worse than those obtained in many classical cases. However, we prove a lower bound, stating that no estimator can attain a better rate of convergence in a minimax sense. For discrete time observations of maximal distance Delta, the Galerkin estimator still attains the above asymptotic rate if Delta is roughly of order T^(-1/2). In contrast, we prove that for observation intervals Delta, with Delta independent of T, the rate must deteriorate significantly by providing the rate estimate T^(-s/(2s+6)) from below. Furthermore, we construct an adaptive estimator by applying wavelet thresholding techniques to the corresponding ill-posed inverse problem. This nonlinear estimator attains the above minimax rate even for more general classes of Besov spaces B^s_(p,infinity) with p>max(6/(2s+3),1). The restriction p >= 6/(2s+3) is shown to hold for any estimator, hence to be inherently associated with the estimation problem. Finally, a hypothesis test with a nonparametric alternative is constructed that could for instance serve to decide whether a trajectory has been generated by a stationary process with or without time delay. The test works for an L^2-separation rate between hypothesis and alternative of order T^(-s/(2s+2.5)). This rate is again shown to be optimal among all conceivable tests. For the proofs, the parameter dependence of the stationary solutions has to be studied in detail and the mapping properties of the associated covariance operators have to be determined exactly. Other results of general interest concern the mixing properties of the stationary solution, a case study for exponential weight functions and the approximation of the stationary process by discrete time autoregressive processes.