Abstract
For the linear regression model we define SM-estimators with the following properties:
With high probability the estimator is identical with the least squares estimator, if the data correspond to the assumption of normality. Especially, the estimation procedure has 95% asymptotic efficiency at the normal model.
The procedure will identify groups of data which do not follow the model, as long as more than 50% of the data are in correspondence with the ideal model. Especially, the SM-estimator has breakdown point 1/2.
We evaluate bounds on the supremum asymptotic bias (SAB) for rather big balls around the ideal model, which will prove uniform consistency, too.
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© 1994 Springer-Verlag Berlin Heidelberg
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Behnen, K. (1994). A Modification of Least Squares with High Efficiency and High Breakdown Point in Linear Regression. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_14
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DOI: https://doi.org/10.1007/978-3-642-57984-4_14
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0770-7
Online ISBN: 978-3-642-57984-4
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