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UBC Theses and Dissertations
A new measure of quantitative robustness Mazzi, Sonia V. T
Abstract
The Gross-Error Sensitivity (GES) and the Breakdown Point (BP) are two measures of quantitative robustness which have played a key role in the development of the theory of robust-ness. Both can be derived from the maximum bias function B(€) and constitute a two-number summary of this function. The GES is the derivative of B(€) at the origin whereas the BP determines the asymptote of the curve (c, B(€)). Since GES€ ≈ B(€) for € near zero, the GES summarizes the behavior of B(€) near the origin. On the other hand, the BP does not provide an approximation for B(€) for c large and, consequently, estimates with strikingly different bias performance when c is large may have the same BP. A new robustness quantifier, the breakdown rate (BR), that summarizes the behavior of B(€)for € near BP will be introduced. The BR for several families of robust estimates of regression will be presented and the increased usefulness of the three-number summary (GES,BP,BR) for comparing robust estimates will be illustrated by several examples.
Item Metadata
Title |
A new measure of quantitative robustness
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1992
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Description |
The Gross-Error Sensitivity (GES) and the Breakdown Point (BP) are two measures of quantitative robustness which have played a key role in the development of the theory of robust-ness. Both can be derived from the maximum bias function B(€) and constitute a two-number summary of this function. The GES is the derivative of B(€) at the origin whereas the BP determines the asymptote of the curve (c, B(€)).
Since GES€ ≈ B(€) for € near zero, the GES summarizes the behavior of B(€) near the origin. On the other hand, the BP does not provide an approximation for B(€) for c large and, consequently, estimates with strikingly different bias performance when c is large may have the same BP.
A new robustness quantifier, the breakdown rate (BR), that summarizes the behavior of B(€)for € near BP will be introduced. The BR for several families of robust estimates of regression will be presented and the increased usefulness of the three-number summary (GES,BP,BR) for comparing robust estimates will be illustrated by several examples.
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Extent |
1482597 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-01-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0086725
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1992-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.