Signed Scale Measures: An Introduction and Application

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Title: Signed Scale Measures: An Introduction and Application
Author: Wilson, David Hunt
Advisors: Dennis Boos, Committee Co-Chair
Jacquelin Dietz, Committee Member
Len Stefanski, Committee Member
Jacqueline Hughes-Oliver, Committee Co-Chair
Paul Bitting, Committee Member
Abstract: The role of the Interquartile Range in constructing a Boxplot provides the rationale for considering the halves of the "box" in a Boxplot. The two halves of the boxplot are viewed as measures of distance from a measure of location. This viewpoint is the genesis for considering a new class of parameters called signed scale parameters. A conceptual framework for signed scale parameters is introduced and four classes of signed scale parameters are discussed in detail. The small sample and asymptotic behaviors for several signed scale estimators are examined for nine distributions. A new Boxplot construction rule that uses one pair of signed scale estimators is introduced. The common, skew adjusted, and signed Boxplots are compared with respect to their propensity to label observations as "outliers" and their ability to provide skewness information.
Date: 2002-11-04
Degree: PhD
Discipline: Statistics

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