Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations
AbstractWe provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contract to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previousdefinitions of breakdown in both linear and non-linear regression settings. Insome cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applied to models for dependent observations (time-series, spatial statistics) where currenty breakdown definitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-040/2.
Date of creation: 12 May 2000
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Bias curve; Linear regression; Non-linear regression; Outliers; Spatial statistics; Statistical robustness; Time series;
Other versions of this item:
- Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94.
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