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A statistical test spectrum
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Text
TitleInfo
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Title
A statistical test spectrum
SubTitle
from robust to powerful
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A
Identifier
ETD_1659
Identifier
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051385
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eng
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theses
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Statistics and Biostatistics
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Statistics
Abstract
The concept of Scale Curve provides a graphical tool for analysis of multivariate data, with a broad range of statistical applications. Recent research in variants of Scale Curves have shown great promise, as they can be easily adapted to build robust non-parametric testing procedures under various scenarios, while preserving good power, and retaining the crucial virtues of easy computation and simple graphical representation.
This thesis investigates the properties of one such variant of Scale Curves, named the Determinant Scale Curve (dsc). It is shown that the dsc can be used to devise non-parametric exact tests for location of multivariate data with a special property (stated in next paragraph), under both one sample and multi-sample setups. Similar ideas are extended to tackle problems in linear regression, where the dsc is used to build tests for significance of the slope parameter.
For all the problems discussed, the dsc's actually provide a whole spectrum of tests. The tests at the rightmost end of the spectrum are shown to be Pitman equivalent to the benchmark most powerful tests for the given problem. As one moves towards the other end, the corresponding tests become progressively more and more robust, i.e. insensitive to outliers. Simulation results show that this robustification does not come with a serious loss of power under most situations.
This thesis investigates the properties of one such variant of Scale Curves, named the Determinant Scale Curve (dsc). It is shown that the dsc can be used to devise non-parametric exact tests for location of multivariate data with a special property (stated in next paragraph), under both one sample and multi-sample setups. Similar ideas are extended to tackle problems in linear regression, where the dsc is used to build tests for significance of the slope parameter.
For all the problems discussed, the dsc's actually provide a whole spectrum of tests. The tests at the rightmost end of the spectrum are shown to be Pitman equivalent to the benchmark most powerful tests for the given problem. As one moves towards the other end, the corresponding tests become progressively more and more robust, i.e. insensitive to outliers. Simulation results show that this robustification does not come with a serious loss of power under most situations.
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electronic resource
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ix, 64 p. : ill.
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Note
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Ph.D.
Note
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Includes bibliographical references (p. 61-63)
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by Somnath Mukherjee
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Mukherjee
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Somnath
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1978
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Somnath Mukherjee
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Singh
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Kesar
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chair
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Advisory Committee
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Kesar Singh
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Tyler
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David
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internal member
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David E Tyler
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Strawderman
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William
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William E. Strawderman
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Zhang
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Jingshan
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Jingshan Zhang
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Rutgers University
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Graduate School - New Brunswick
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school
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2009
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2009-05
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xx
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Rutgers University Electronic Theses and Dissertations
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ETD
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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doi:10.7282/T3XW4K1F
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ETD doctoral
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The author owns the copyright to this work.
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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