Survey data can be viewed as incomplete or partially missing from a variety of perspectives and there are different ways of dealing with this kind of data in the prediction and the estimation of economic quantities. In this thesis, we present two selected research contexts in which the prediction or estimation of economic quantities is examined under incomplete survey data. These contexts are first the investigation of composite estimators in the German Microcensus (Chapters 3 and 4) and second extensions of multivariate Fay-Herriot (MFH) models (Chapters 5 and 6), which are applied to small area problems. Composite estimators are estimation methods that take into account the sample overlap in rotating panel surveys such as the German Microcensus in order to stabilise the estimation of the statistics of interest (e.g. employment statistics). Due to the partial sample overlaps, information from previous samples is only available for some of the respondents, so the data are partially missing. MFH models are model-based estimation methods that work with aggregated survey data in order to obtain more precise estimation results for small area problems compared to classical estimation methods. In these models, several variables of interest are modelled simultaneously. The survey estimates of these variables, which are used as input in the MFH models, are often partially missing. If the domains of interest are not explicitly accounted for in a sampling design, the sizes of the samples allocated to them can, by chance, be small. As a result, it can happen that either no estimates can be calculated at all or that the estimated values are not published by statistical offices because their variances are too large.

Data fusions are becoming increasingly relevant in official statistics. The aim of a data fusion is to combine two or more data sources using statistical methods in order to be able to analyse different characteristics that were not jointly observed in one data source. Record linkage of official data sources using unique identifiers is often not possible due to methodological and legal restrictions. Appropriate data fusion methods are therefore of central importance in order to use the diverse data sources of official statistics more effectively and to be able to jointly analyse different characteristics. However, the literature lacks comprehensive evaluations of which fusion approaches provide promising results for which data constellations. Therefore, the central aim of this thesis is to evaluate a concrete plethora of possible fusion algorithms, which includes classical imputation approaches as well as statistical and machine learning methods, in selected data constellations. To specify and identify these data contexts, data and imputation-related scenario types of a data fusion are introduced: Explicit scenarios, implicit scenarios and imputation scenarios. From these three scenario types, fusion scenarios that are particularly relevant for official statistics are selected as the basis for the simulations and evaluations. The explicit scenarios are the fulfilment or violation of the Conditional Independence Assumption (CIA) and varying sample sizes of the data to be matched. Both aspects are likely to have a direct, that is, explicit, effect on the performance of different fusion methods. The summed sample size of the data sources to be fused and the scale level of the variable to be imputed are considered as implicit scenarios. Both aspects suggest or exclude the applicability of certain fusion methods due to the nature of the data. The univariate or simultaneous, multivariate imputation solution and the imputation of artificially generated or previously observed values in the case of metric characteristics serve as imputation scenarios. With regard to the concrete plethora of possible fusion algorithms, three classical imputation approaches are considered: Distance Hot Deck (DHD), the Regression Model (RM) and Predictive Mean Matching (PMM). With Decision Trees (DT) and Random Forest (RF), two prominent tree-based methods from the field of statistical learning are discussed in the context of data fusion. However, such prediction methods aim to predict individual values as accurately as possible, which can clash with the primary objective of data fusion, namely the reproduction of joint distributions. In addition, DT and RF only comprise univariate imputation solutions and, in the case of metric variables, artificially generated values are imputed instead of real observed values. Therefore, Predictive Value Matching (PVM) is introduced as a new, statistical learning-based nearest neighbour method, which could overcome the distributional disadvantages of DT and RF, offers a univariate and multivariate imputation solution and, in addition, imputes real and previously observed values for metric characteristics. All prediction methods can form the basis of the new PVM approach. In this thesis, PVM based on Decision Trees (PVM-DT) and Random Forest (PVM-RF) is considered. The underlying fusion methods are investigated in comprehensive simulations and evaluations. The evaluation of the various data fusion techniques focusses on the selected fusion scenarios. The basis for this is formed by two concrete and current use cases of data fusion in official statistics, the fusion of EU-SILC and the Household Budget Survey on the one hand and of the Tax Statistics and the Microcensus on the other. Both use cases show significant differences with regard to different fusion scenarios and thus serve the purpose of covering a variety of data constellations. Simulation designs are developed from both use cases, whereby the explicit scenarios in particular are incorporated into the simulations. The results show that PVM-RF in particular is a promising and universal fusion approach under compliance with the CIA. This is because PVM-RF provides satisfactory results for both categorical and metric variables to be imputed and also offers a univariate and multivariate imputation solution, regardless of the scale level. PMM also represents an adequate fusion method, but only in relation to metric characteristics. The results also imply that the application of statistical learning methods is both an opportunity and a risk. In the case of CIA violation, potential correlation-related exaggeration effects of DT and RF, and in some cases also of RM, can be useful. In contrast, the other methods induce poor results if the CIA is violated. However, if the CIA is fulfilled, there is a risk that the prediction methods RM, DT and RF will overestimate correlations. The size ratios of the studies to be fused in turn have a rather minor influence on the performance of fusion methods. This is an important indication that the larger dataset does not necessarily have to serve as a donor study, as was previously the case. The results of the simulations and evaluations provide concrete implications as to which data fusion methods should be used and considered under the selected data and imputation constellations. Science in general and official statistics in particular benefit from these implications. This is because they provide important indications for future data fusion projects in order to assess which specific data fusion method could provide adequate results along the data constellations analysed in this thesis. Furthermore, with PVM this thesis offers a promising methodological innovation for future data fusions and for imputation problems in general.