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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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