Resampling

Resampling (englisch) bzw. Stichprobenwiederholung bezeichnet die Bestimmung der statistischen Eigenschaften von Stichprobenfunktionen, wie Schätzern oder Testgrößen auf Basis einer wiederholten Ziehung von Stichproben, sogenannten Unterstichproben, aus einer Ausgangsstichprobe. Die Stichprobenfunktion wird auf Basis der gezogenen Unterstichproben wiederholt berechnet[1] und anhand der Ergebnisse ihre Verteilungseigenschaften untersucht. Vorteilhaft ist hierbei, dass beim Resampling keine Verteilung angenommen werden muss, wodurch die Verfahren sehr breit einsetzbar sind und (im Gegensatz zu Methoden der parametrischen Statistik) vergleichsweise wenige Annahmen getroffen werden müssen.

Monte-Carlo-Simulationen

Für das Resampling werden typischerweise rechnergestützte statistische Auswertungsmethoden genutzt. Man benötigt sie, da die Wahrscheinlichkeitsverteilung einer Stichprobenfunktion oder eines statistischen Tests nicht immer (mit vertretbarem Aufwand) bestimmt werden kann. Um auch in diesen Situationen Vertrauensintervalle angeben und Tests durchführen zu können, werden auf der Grundlage der vorhandenen Daten mit Hilfe von Monte-Carlo-Simulationen große Anzahlen von (Pseudo-Zufalls-)Datensätzen erzeugt (das Resampling). Diese werden dann verwendet, um die Verteilung der Stichprobenfunktion, insbesondere deren Streuungsparameter, zu schätzen.

Die Verfahren werden seit den 1980er Jahren entwickelt. Bekannte Verfahren sind die Jackknife-Methode und das als Verbesserung entstandene Bootstrapping-Verfahren.

Resampling-Verfahren

Verschiedene Verfahren werden zu den Resampling-Methoden gezählt.

Anwendungen

Einzelnachweise

  1. ↑ Bernd Rönz, Hans G. Strohe (1994), Lexikon Statistik, Gabler Verlag, S. 312.

Literatur

  • Y. Shao, D. Tu: The Jackknife and Bootstrap. Springer, New York, 1995
  • B. Efron, R.G. Tibshirani: An Introduction to the Bootstrap. Chapman and Hall, New York, 1993
  • E. F. Harrell: Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis, Springer, New York, 2006
  • Jiang W, Simon R. A comparison of bootstrap methods and an adjusted bootstrap approach for estimating the prediction error in microarray classification. Stat Med. 2007 Dec 20;26(29):5320-34. doi:10.1002/sim.2968. PMID 17624926. https://brb.nci.nih.gov/techreport/prederr_rev_0407.pdf

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