Semi-orderings between distribution functions and their application to robustness of parameter estimators

1 January 1975

journal article
research article
Published by Taylor & Francis in Mathematische Operationsforschung und Statistik

Vol. 6 (2) , 179-188
https://doi.org/10.1080/02331887508801208

Abstract

A random variable Y with the distribution P _Y⊝ is considered. Based on a sample we have to astimate ψ(⊝). We look for optimal estimators which are robust against the loss function and robust against the sample distribution. A suitable approach for this are semi-orderings between distribution functions closely relsted to convex or monotone loss functions. The obtained results are applicable to estimators in the linear regression model, especially to the robutness of the usual GAUSS-MARKOV-estimator.

Keywords

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