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Analysis of variance of paired data without repetition of measurement

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Analysis of variance of paired data without repetition of measurement

Content Provider	Springer Nature Link
Author	Martin, Klaus Böckenhoff, Annette
Copyright Year	2006
Abstract	The objective of this analysis of variance of paired data is to estimate positive random error variances for each ofN=2 measurement methods. The two methods measure the same item only once without measurement repetition. The well-known unbiased Grubbs’ estimators are not suitable for practical purpose because they can become negative. With the help of Chebyshev’s inequality the probability was determined that Grubbs’ estimators become negative. Based on the Grubbs’ estimators new estimators were derived. The new estimators are indeed always positive, but they are biased. It is shown that the biases are small. In case the Grubbs’ estimators are positive a bias correction of the new estimators may be envisaged.Das Ziel dieser Varianzanalyse von gepaarten Messungen ist die Schätzung zufälliger Messfehlervarianzen für jede derN=2 Messmethoden. Die beiden Messmethoden messen das gleiche Merkmal eines Elements nur einmal ohne Messwiederholung. Die bekannten unverzerrten Grubbs-Schätzer sind für die praktische Anwendung nicht geeignet, weil sie negativ werden könnten. Die Tschebyscheffsche Ungleichung wurde genutzt, um die Wahrscheinlichkeit zu ermitteln, dass Grubbs-Schätzer negativ werden. Basierend auf Grubbs-Schätzern wurden neue Schätzer hergeleitet. Diese neuen Schätzer sind zwar immer positiv, aber verzerrt. Es wird gezeigt, dass die Verzerrungen klein sind. Für den Fall, dass die Grubbs-Schätzer positiv ausfallen, könnte eine Korrektur der Verzerrung in Betracht gezogen werden.
Ending Page	384
Page Count	20
Starting Page	365
File Format	PDF
ISSN	00026018
e-ISSN	16140176
Journal	AStA Advances in Statistical Analysis
Issue Number	3
Volume Number	90
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	Subscribed
Subject Keyword	Estimation: General paired data random measurement error variances Statistics for Business/Economics/Mathematical Finance/Insurance Econometric and Statistical Methods and Methodology: General Probability Theory and Stochastic Processes precision and bias correction Econometrics Statistics Analysis of variance product variability
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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