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

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  • Hansohm, Jürgen
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    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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    Bibliographic Info

    Paper provided by Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie in its series Arbeitspapiere zur mathematischen Wirtschaftsforschung with number 187.

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    Date of creation: 2004
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    Handle: RePEc:zbw:augamw:187

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    Web page: http://www.wiwi.uni-augsburg.de/bwl/bamberg/
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    1. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer, vol. 41(4), pages 505-529, December.
    2. 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, vol. 43(2), pages 279-281, June.
    3. Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer, vol. 46(4), pages 357-388, December.
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