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Glättung mit diskreten Daten: Kernfunktionen in Dichteschätzproblemen, nonparametrischer Regression und Diskriminanzanalyse

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Book cover Multivariate Modelle

Part of the book series: Medizinische Informatik, Biometrie und Epidemiologie ((MEDINFO,volume 74))

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Zusammenfassung

Diskrete Kernfunktionen werden als Instrument der Dichteschätzung für kategoriale Variablen entwickelt. Die Darstellung als lineare Transformationen der relativen Häufigkeit zeigt die Ähnlichkeit zu alternativen Glättungsverfahren. Da Dichteschätzung allein meist nicht Endzweck einer Datenanalyse ist, wird der Einsatz der Verfahren in den komplexeren Problemstellungen der Regressions- und Diskriminanzanalyse betrachtet. Dichteschätzer sind ein entscheidender Baustein für den Kernregressionsschätzer. Die Güte dieses Verfahrens der non- parametrischen kategorialen Regression wird entscheidend von der Wahl der Glättungsparameter beeinflußt - dieser Einfluß und alternative Auswahlverfahren werden untersucht. Ein kurzer Abschnitt zeigt die Anwendbarkeit im Bereich der Verweildaueranalyse. Als Baustein der Diskriminanzanalyse läßt sich Kerndichteschätzung auf zweifache Art einsetzen: als direktes Verfahren zur Schätzung der a posteriori-Wahrscheinlichkeit und als indirektes Verfahren zur Schätzung der Merkmalsverteilung in den zu prognostizierenden Klassen. Für beide Möglichkeiten werden Wahlmöglichkeiten für den Glättungsparameter entwickelt.

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Authors and Affiliations

  1. Lehrstuhl für Statistik, Universität Regensburg, Universitätsstraße 31, D-8400, Regensburg, Deutschland

    Gerhard Tutz

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  1. Gerhard Tutz
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Editors and Affiliations

  1. Institut für Statistik, Leopold-Franzens Universität Innsbruck, Innrain 52, A-6020, Innsbruck, Austria

    Gilg U. H. Seeber

  2. Institut für Sozial- und Präventivmedizin, Universität Bern, Finkenhubelweg 11, CH-3012, Bern, Switzerland

    Christoph E. Minder

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© 1991 Springer-Verlag Berlin Heidelberg

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Tutz, G. (1991). Glättung mit diskreten Daten: Kernfunktionen in Dichteschätzproblemen, nonparametrischer Regression und Diskriminanzanalyse. In: Seeber, G.U.H., Minder, C.E. (eds) Multivariate Modelle. Medizinische Informatik, Biometrie und Epidemiologie, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95669-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-95669-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54511-8

  • Online ISBN: 978-3-642-95669-0

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