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• W1505397311 abstract "This chapter discusses positive-breakdown methods. It focusses on the linear regression model. The goal of positive-breakdown methods is to be robust against the possibility of one or several unannounced outliers that may occur anywhere in the data. High-breakdown regression does not throw away 50% of the data, but instead it finds a majority fit, which can then be used to detect the actual outliers. The purpose of positive-breakdown method is not to delete and forget the points outside the tolerance band but to study the residual plot. An example of simple regression is illustrated in the chapter to explain the behavior of least median of squares method (LMS) and the corresponding residuals. Positive-breakdown regression methods, such as LMS, can be extended to models with several intercepts and to models including dummy regressors. Rousseeuw and Leroy applied the LMS and the least trimmed squares method to the zero-intercept regression model, to autoregressive time series, to orthogonal regression, and to directional data. Other extensions are to nonparametric regression, nonlinear regression, alternating regression, and logistic regression. For univariate scale estimation, two new methods were proposed recently. They combine the advantages of the median absolute deviation with two extra features: a higher efficiency and suitability for symmetric as well as asymmetric data distributions." @default.
• W1505397311 created "2016-06-24" @default.
• W1505397311 creator A5075121395 @default.
• W1505397311 date "1997-01-01" @default.
• W1505397311 modified "2023-10-17" @default.
• W1505397311 title "5 Introduction to positive-breakdown methods" @default.
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• W1505397311 doi "https://doi.org/10.1016/s0169-7161(97)15007-6" @default.
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