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Algorithmus und Programm zur Bestimmung der monotonen Kleinst-Quadrate Lösung bei partiellen Präordnungen

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  • Hansohm, Jürgen

Abstract

Sei A = {1, . . . , n} eine endliche Menge und f : A --> IR gegeben. Im folgenden Beitrag werden Algorithmen zur Ermittlung der Kleinst-Quadrate Regression g : A --> IR von f beschrieben, wobei g monoton bzgl. einer nicht notwendigerweise vollständigen Präordnung auf A ist. Neben den theoretischen Grundlagen und dem allgemeinen Fall werden auch die Spezialfälle der hierarchischen und vollständigen Präordnung beschrieben. Darüber hinaus werden Fehlerabschätzungen zum Optimum angegeben. Sämtliche Algorithmen sind in dem Modul PartOrder implementiert, dessen Anwendung an einem Beispiel kurz beschrieben wird. Das Modul basiert auf dem .NET Framework und kann unter verschiedenen Programmiersprachen (Visual Basic, C++, C#, etc.) aufgerufen werden.

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  • Hansohm, Jürgen, 2004. "Algorithmus und Programm zur Bestimmung der monotonen Kleinst-Quadrate Lösung bei partiellen Präordnungen," Arbeitspapiere zur mathematischen Wirtschaftsforschung 187, Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie.
  • Handle: RePEc:zbw:augamw:187
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    1. Forrest Young & Yoshio Takane & Jan Leeuw, 1978. "The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 279-281, June.
    2. Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 357-388, December.
    3. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
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