310 Sammlungen allgemeiner Statistiken
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Official business surveys form the basis for national and regional business statistics and are thus of great importance for analysing the state and performance of the economy. However, both the heterogeneity of business data and their high dynamics pose a particular challenge to the feasibility of sampling and the quality of the resulting estimates. A widely used sampling frame for creating the design of an official business survey is an extract from an official business register. However, if this frame does not accurately represent the target population, frame errors arise. Amplified by the heterogeneity and dynamics of business populations, these errors can significantly affect the estimation quality and lead to inefficiencies and biases. This dissertation therefore deals with design-based methods for optimising business surveys with respect to different types of frame errors.
First, methods for adjusting the sampling design of business surveys are addressed. These approaches integrate auxiliary information about the expected structures of frame errors into the sampling design. The aim is to increase the number of sampled businesses that are subject to frame errors. The element-specific frame error probability is estimated based on auxiliary information about frame errors observed in previous samples. The approaches discussed consider different types of frame errors and can be incorporated into predefined designs with fixed strata.
As the second main pillar of this work, methods for adjusting weights to correct for frame errors during estimation are developed and investigated. As a result of frame errors, the assumptions under which the original design weights were determined based on the sampling design no longer hold. The developed methods correct the design weights taking into account the errors identified for sampled elements. Case-number-based reweighting approaches, on the one hand, attempt to reconstruct the unknown size of the individual strata in the target population. In the context of weight smoothing methods, on the other hand, design weights are modelled and smoothed as a function of target or auxiliary variables. This serves to avoid inefficiencies in the estimation due to highly scattering weights or weak correlations between weights and target variables. In addition, possibilities of correcting frame errors by calibration weighting are elaborated. Especially when the sampling frame shows over- and/or undercoverage, the inclusion of external auxiliary information can provide a significant improvement of the estimation quality. For those methods whose quality cannot be measured using standard procedures, a procedure for estimating the variance based on a rescaling bootstrap is proposed. This enables an assessment of the estimation quality when using the methods in practice.
In the context of two extensive simulation studies, the methods presented in this dissertation are evaluated and compared with each other. First, in the environment of an experimental simulation, it is assessed which approaches are particularly suitable with regard to different data situations. In a second simulation study, which is based on the structural survey in the services sector, the applicability of the methods in practice is evaluated under realistic conditions.
The Eurosystem's Household Finance and Consumption Survey (HFCS) collects micro data on private households' balance sheets, income and consumption. It is a stylised fact that wealth is unequally distributed and that the wealthiest own a large share of total wealth. For sample surveys which aim at measuring wealth and its distribution, this is a considerable problem. To overcome it, some of the country surveys under the HFCS umbrella try to sample a disproportionately large share of households that are likely to be wealthy, a technique referred to as oversampling. Ignoring such types of complex survey designs in the estimation of regression models can lead to severe problems. This thesis first illustrates such problems using data from the first wave of the HFCS and canonical regression models from the field of household finance and gives a first guideline for HFCS data users regarding the use of replicate weight sets for variance estimation using a variant of the bootstrap. A further investigation of the issue necessitates a design-based Monte Carlo simulation study. To this end, the already existing large close-to-reality synthetic simulation population AMELIA is extended with synthetic wealth data. We discuss different approaches to the generation of synthetic micro data in the context of the extension of a synthetic simulation population that was originally based on a different data source. We propose an additional approach that is suitable for the generation of highly skewed synthetic micro data in such a setting using a multiply-imputed survey data set. After a description of the survey designs employed in the first wave of the HFCS, we then construct new survey designs for AMELIA that share core features of the HFCS survey designs. A design-based Monte Carlo simulation study shows that while more conservative approaches to oversampling do not pose problems for the estimation of regression models if sampling weights are properly accounted for, the same does not necessarily hold for more extreme oversampling approaches. This issue should be further analysed in future research.
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.
The dissertation deals with methods to improve design-based and model-assisted estimation techniques for surveys in a finite population framework. The focus is on the development of the statistical methodology as well as their implementation by means of tailor-made numerical optimization strategies. In that regard, the developed methods aim at computing statistics for several potentially conflicting variables of interest at aggregated and disaggregated levels of the population on the basis of one single survey. The work can be divided into two main research questions, which are briefly explained in the following sections.
First, an optimal multivariate allocation method is developed taking into account several stratification levels. This approach results in a multi-objective optimization problem due to the simultaneous consideration of several variables of interest. In preparation for the numerical solution, several scalarization and standardization techniques are presented, which represent the different preferences of potential users. In addition, it is shown that by solving the problem scalarized with a weighted sum for all combinations of weights, the entire Pareto frontier of the original problem can be generated. By exploiting the special structure of the problem, the scalarized problems can be efficiently solved by a semismooth Newton method. In order to apply this numerical method to other scalarization techniques as well, an alternative approach is suggested, which traces the problem back to the weighted sum case. To address regional estimation quality requirements at multiple stratification levels, the potential use of upper bounds for regional variances is integrated into the method. In addition to restrictions on regional estimates, the method enables the consideration of box-constraints for the stratum-specific sample sizes, allowing minimum and maximum stratum-specific sampling fractions to be defined.
In addition to the allocation method, a generalized calibration method is developed, which is supposed to achieve coherent and efficient estimates at different stratification levels. The developed calibration method takes into account a very large number of benchmarks at different stratification levels, which may be obtained from different sources such as registers, paradata or other surveys using different estimation techniques. In order to incorporate the heterogeneous quality and the multitude of benchmarks, a relaxation of selected benchmarks is proposed. In that regard, predefined tolerances are assigned to problematic benchmarks at low aggregation levels in order to avoid an exact fulfillment. In addition, the generalized calibration method allows the use of box-constraints for the correction weights in order to avoid an extremely high variation of the weights. Furthermore, a variance estimation by means of a rescaling bootstrap is presented.
Both developed methods are analyzed and compared with existing methods in extensive simulation studies on the basis of a realistic synthetic data set of all households in Germany. Due to the similar requirements and objectives, both methods can be successively applied to a single survey in order to combine their efficiency advantages. In addition, both methods can be solved in a time-efficient manner using very comparable optimization approaches. These are based on transformations of the optimality conditions. The dimension of the resulting system of equations is ultimately independent of the dimension of the original problem, which enables the application even for very large problem instances.