University-GH, Diss.--Paderborn, 1999.

Berlin, Humboldt-Universiẗat, Diss., 1999.

Berlin, Freie University, Diss., 2001. / Dateiformat: zip, Dateien im PDF-Format.

Bielefeld, Universiẗat, Diss., 2004.

<p>The quality of sample survey results is to a large degree dependent on decisions made by survey statisticians at the planning stage. The first paper studies two issues related to the planning stage: (i) the sensitivity of model assumptions concerning the relation between the size measure and a study variable in without replacement probability proportional-to-size sampling (π<i>p</i>s sampling), and (ii) properties of practicable sample selection schemes for fixed size π<i>p</i>s sampling. These two issues are also addressed in the second paper, which furthermore discusses the consequences of the presence of more than one study variable and to what extent the auxiliary information used in the design and that used in the estimators interact.</p><p>The evident problem in both the first and the second paper is how to choose an overall efficient sampling design when there are several important study variables with various relationships to the available auxiliary variables. The third paper suggests a diagnostic tool to support the choice of design, and on the basis of three criteria of overall efficiency optimal designs are derived.</p><p>The optimal designs presented in the third paper may not be fully satisfactory in meeting specified precision requirements for separate estimators. To achieve a design that is tailor-made to meet such requirements, optimisation must be done under restrictions. Though the underlying optimisation problem is only outlined in paper III, a solution involving non-linear programming methods is given in the fourth paper. By way of an example based on an application to a Swedish business population, the fourth paper compares a design obtained through non-linear programming algorithms with designs discussed in paper III as well as designs based on the same principal ideas as those discussed in the first two papers. The paper suggests a flexible solution regarding how to use auxiliary information exhaustively and to provide diagnostic support for the final design choice.</p>

The quality of sample survey results is to a large degree dependent on decisions made by survey statisticians at the planning stage. The first paper studies two issues related to the planning stage: (i) the sensitivity of model assumptions concerning the relation between the size measure and a study variable in without replacement probability proportional-to-size sampling (πps sampling), and (ii) properties of practicable sample selection schemes for fixed size πps sampling. These two issues are also addressed in the second paper, which furthermore discusses the consequences of the presence of more than one study variable and to what extent the auxiliary information used in the design and that used in the estimators interact. The evident problem in both the first and the second paper is how to choose an overall efficient sampling design when there are several important study variables with various relationships to the available auxiliary variables. The third paper suggests a diagnostic tool to support the choice of design, and on the basis of three criteria of overall efficiency optimal designs are derived. The optimal designs presented in the third paper may not be fully satisfactory in meeting specified precision requirements for separate estimators. To achieve a design that is tailor-made to meet such requirements, optimisation must be done under restrictions. Though the underlying optimisation problem is only outlined in paper III, a solution involving non-linear programming methods is given in the fourth paper. By way of an example based on an application to a Swedish business population, the fourth paper compares a design obtained through non-linear programming algorithms with designs discussed in paper III as well as designs based on the same principal ideas as those discussed in the first two papers. The paper suggests a flexible solution regarding how to use auxiliary information exhaustively and to provide diagnostic support for the final design choice.

Bei vielen Fragestellungen, in denen sich eine Grundgesamtheit in verschiedene Klassen unterteilt, ist weniger die relative Klassengröße als vielmehr die Anzahl der Klassen von Bedeutung. So interessiert sich beispielsweise der Biologe dafür, wie viele Spezien einer Gattung es gibt, der Numismatiker dafür, wie viele Münzen oder Münzprägestätten es in einer Epoche gab, der Informatiker dafür, wie viele unterschiedlichen Einträge es in einer sehr großen Datenbank gibt, der Programmierer dafür, wie viele Fehler eine Software enthält oder der Germanist dafür, wie groß der Wortschatz eines Autors war oder ist. Dieser Artenreichtum ist die einfachste und intuitivste Art und Weise eine Population oder Grundgesamtheit zu charakterisieren. Jedoch kann nur in Kollektiven, in denen die Gesamtanzahl der Bestandteile bekannt und relativ klein ist, die Anzahl der verschiedenen Spezien durch Erfassung aller bestimmt werden. In allen anderen Fällen ist es notwendig die Spezienanzahl durch Schätzungen zu bestimmen.

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