This dissertation deals with consistent estimates in household surveys. Household surveys are often drawn via cluster sampling, with households sampled at the first stage and persons selected at the second stage. The collected data provide information for estimation at both the person and the household level. However, consistent estimates are desirable in the sense that the estimated household-level totals should coincide with the estimated totals obtained at the person-level. Current practice in statistical offices is to use integrated weighting. In this approach consistent estimates are guaranteed by equal weights for all persons within a household and the household itself. However, due to the forced equality of weights, the individual patterns of persons are lost and the heterogeneity within households is not taken into account. In order to avoid the negative consequences of integrated weighting, we propose alternative weighting methods in the first part of this dissertation that ensure both consistent estimates and individual person weights within a household. The underlying idea is to limit the consistency conditions to variables that emerge in both the personal and household data sets. These common variables are included in the person- and household-level estimator as additional auxiliary variables. This achieves consistency more directly and only for the relevant variables, rather than indirectly by forcing equal weights on all persons within a household. Further decisive advantages of the proposed alternative weighting methods are that original individual rather than the constructed aggregated auxiliaries are utilized and that the variable selection process is more flexible because different auxiliary variables can be incorporated in the person-level estimator than in the household-level estimator. In the second part of this dissertation, the variances of a person-level GREG estimator and an integrated estimator are compared in order to quantify the effects of the consistency requirements in the integrated weighting approach. One of the challenges is that the estimators to be compared are of different dimensions. The proposed solution is to decompose the variance of the integrated estimator into the variance of a reduced GREG estimator, whose underlying model is of the same dimensions as the person-level GREG estimator, and add a constructed term that captures the effects disregarded by the reduced model. Subsequently, further fields of application for the derived decomposition are proposed such as the variable selection process in the field of econometrics or survey statistics.

Competitive analysis is a well known method for analyzing online algorithms. Two online optimization problems, the scheduling problems and the list accessing problems, are considered in the thesis of Yida Zhu in the respect of this method. For both problems, several existing online and offline algorithms are studied. Their performances are compared with the performances of corresponding offline optimal algorithms. In particular, the list accessing algorithm BIT is carefully reviewed. The classical proof of its worst case performance get simplified by adapting the knowledge about the optimal offline algorithm. With regard to average case analysis, a new closed formula is developed to determine the performance of BIT on specific class of instances. All algorithm considered in this thesis are also implemented in Julia. Their empirical performances are studied and compared with each other directly.

Die publikationsbasierte Dissertation untersucht die Bedeutung sozialer Bewegungen für die Entwicklung der Sozialen Arbeit am Ende des 19. und den ersten Jahrzehnten des 20. Jahrhunderts als Profession und Disziplin in den USA und in Deutschland. Dabei wird die entstehende Soziale Arbeit als ‚Formbildung‘ sozialer Bewegungen verstanden und gefragt, wie sich die Bewegungen in die sich etablierende und institutionalisierende Profession und Wissenschaft Soziale Arbeit einschreiben, welche Anliegen dabei verfolgt werden und wie dadurch Wissen in der Sozialen Arbeit auch über nationalstaatliche Grenzen hinweg zirkuliert. Die Untersuchung konzentriert sich auf Prozesse der Pädagogisierung, also unterschiedliche ‚Formbildungen des Pädagogischen‘, die die Bewegungsanliegen zum Thema von Aufklärung, (Selbst)Bildung und Pädagogik machen, und auf solche der Verwissenschaftlichung, die sich auf den Aufbau einer Wissensgrundlage zur Bearbeitung von sozialen Problemen richten und dabei alternative Formen der Wissensproduktion ausbilden. Diese Prozesse werden in drei Teilstudien – zur Charity Organization Movement und der Settlement House Movement in den USA sowie der bürgerlichen Frauenbewegung in Deutschland – in sieben Einzelbeiträgen näher untersucht. Im Mittelpunkt stehen dabei die Handlungsmethoden und das Praxisverständnis sowie Forschungskonzepte und –projekte exemplarisch ausgewählter sozialbewegter Initiativen der Sozialen Arbeit. Dabei werden unter anderem nicht-intendierte Effekte untersucht, die zum Beispiel in Konservierungen normativer Vorstellungen und Ideologien in als demokratisierend angelegten Ansätzen, aber auch in ‚differenzverstärkenden‘ Effekten bestehen können.

Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations. The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization. Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits. The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings. Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.

We consider a linear regression model for which we assume that some of the observed variables are irrelevant for the prediction. Including the wrong variables in the statistical model can either lead to the problem of having too little information to properly estimate the statistic of interest, or having too much information and consequently describing fictitious connections. This thesis considers discrete optimization to conduct a variable selection. In light of this, the subset selection regression method is analyzed. The approach gained a lot of interest in recent years due to its promising predictive performance. A major challenge associated with the subset selection regression is the computational difficulty. In this thesis, we propose several improvements for the efficiency of the method. Novel bounds on the coefficients of the subset selection regression are developed, which help to tighten the relaxation of the associated mixed-integer program, which relies on a Big-M formulation. Moreover, a novel mixed-integer linear formulation for the subset selection regression based on a bilevel optimization reformulation is proposed. Finally, it is shown that the perspective formulation of the subset selection regression is equivalent to a state-of-the-art binary formulation. We use this insight to develop novel bounds for the subset selection regression problem, which show to be highly effective in combination with the proposed linear formulation. In the second part of this thesis, we examine the statistical conception of the subset selection regression and conclude that it is misaligned with its intention. The subset selection regression uses the training error to decide on which variables to select. The approach conducts the validation on the training data, which oftentimes is not a good estimate of the prediction error. Hence, it requires a predetermined cardinality bound. Instead, we propose to select variables with respect to the cross-validation value. The process is formulated as a mixed-integer program with the sparsity becoming subject of the optimization. Usually, a cross-validation is used to select the best model out of a few options. With the proposed program the best model out of all possible models is selected. Since the cross-validation is a much better estimate of the prediction error, the model can select the best sparsity itself. The thesis is concluded with an extensive simulation study which provides evidence that discrete optimization can be used to produce highly valuable predictive models with the cross-validation subset selection regression almost always producing the best results.