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Breakdown and Groups
, 2002
"... The concept of breakdown point was... In this paper we argue that this success is intimately connected to the fact that the translation and affine groups act on the sample space and give rise to a definition of equivariance for statistical functionals. For such functionals a nontrivial upper bound f ..."
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Cited by 9 (2 self)
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The concept of breakdown point was... In this paper we argue that this success is intimately connected to the fact that the translation and affine groups act on the sample space and give rise to a definition of equivariance for statistical functionals. For such functionals a nontrivial upper bound for the breakdown point can be shown. In the absence of such a group structure a breakdown point of one is attainable and this is perhaps the decisive reason why the concept of breakdown point in other situations has not proved as successful. Even if a natural group is present it is often not sufficiently large to allow a nontrivial upper bound for the breakdown point. One exception to this is the problem of the autocorrelation structure of time series where we derive a nontrivial upper breakdown point using the group of realizable linear filters. The paper is formulated in an abstract manner to emphasize the role of the group and the resulting equivariance structure
Identification of Outliers in a OneWay Random Effects Model
"... We distinguish between three types of outliers in a oneway random effects model. These are formally described in terms of their position relative to the main part of the observations. We propose simple rules for identifying such outliers and give an example which involves medianbased statistics. ..."
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Cited by 2 (0 self)
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We distinguish between three types of outliers in a oneway random effects model. These are formally described in terms of their position relative to the main part of the observations. We propose simple rules for identifying such outliers and give an example which involves medianbased statistics.
Statistical Procedures and Robust Statistics
, 2002
"... It is argued that a main aim of statistics is to produce statistical procedures which in this article are de ned as are de ned as algorithms with inputs and outputs. The structure and properties of such procedures are investigated with special reference to topological and testing considerations ..."
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Cited by 1 (0 self)
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It is argued that a main aim of statistics is to produce statistical procedures which in this article are de ned as are de ned as algorithms with inputs and outputs. The structure and properties of such procedures are investigated with special reference to topological and testing considerations.
Regressions
"... Abstract: In this paper a robust approach for fitting multiplicative models is presented. Focus is on the factor analysis model, where we will estimate factor loadings and scores by a robust alternating regression algorithm. The approach is highly robust, and also works well when there are more vari ..."
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Abstract: In this paper a robust approach for fitting multiplicative models is presented. Focus is on the factor analysis model, where we will estimate factor loadings and scores by a robust alternating regression algorithm. The approach is highly robust, and also works well when there are more variables than observations. The technique yields a robust biplot, depicting the interaction structure between individuals and variables. This biplot is not predetermined by outliers, which can be retrieved from the residual plot. Also provided is an accompanying robust R2plot to determine the appropriate number of factors. The approach is illustrated by real and artificial examples and compared with factor analysis based on robust covariance matrix estimators. The same estimation technique can fit models with both additive and multiplicative effects (FANOVA models) to twoway tables, thereby extending the median polish technique.
THE BREAKDOWN POINT — EXAMPLES AND COUNTEREXAMPLES
"... • The breakdown point plays an important though at times controversial role in statistics. In situations in which it has proved most successful there is a group of transformations which act on the sample space and which give rise to an equivariance structure. For equivariant functionals, that is t ..."
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• The breakdown point plays an important though at times controversial role in statistics. In situations in which it has proved most successful there is a group of transformations which act on the sample space and which give rise to an equivariance structure. For equivariant functionals, that is those functionals which respect the group structure, a nontrivial upper bound for the breakdown point was derived in Davies and Gather (2005). The present paper briefly repeats the main results of Davies and Gather (2005) but is mainly concerned with giving additional insight into the concept of breakdown point. In particular, we discuss the attainability of the bound and the dependence of the breakdown point on the sample or distribution and on the metrics used in its definition. KeyWords: • equivariance; breakdown point; robust statistics. AMS Subject Classification: