Contributions to the theory of statistical breakdown
He, Xu-ming
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https://hdl.handle.net/2142/23662
Description
Title
Contributions to the theory of statistical breakdown
Author(s)
He, Xu-ming
Issue Date
1989
Doctoral Committee Chair(s)
Portnoy, Stephen L.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
The theory of statistical breakdown is studied from two different angles. Firstly, the finite sample breakdown points of estimators are found to be inherently related to their tail performances. This connection provides persuasive new evidence for the importance of the breakdown point of estimators in the assessment of quantitative robustness. Secondly, breakdown robustness for statistical tests is studied via the power and level breakdown functions for the test functionals. This analysis clarifies and unifies various robust aspects in the context of hypotheses testing, and provides more informative robust measures for and new insights into statistical tests. Applications to location-scale problems, the one-way layout and the linear regression model are studied. Motivations and implications of these analyses are discussed.
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