×

Parametric robustness: Small biases can be worthwhile. (English) Zbl 0545.62028

This paper deals with the estimation of the parameters of a Gaussian linear model \(M_ 0\) entertaining the possibility that \(M_ 0\) is invalid and a larger model \(M_ 1\) should be assumed. Estimates are robust if their maximum risk over \(M_ 1\) is finite and the most robust estimate is the least square estimate under \(M_ 1.\)
The author applies robustness ideas of Hodges/Lehmann and Efron/Morris to obtain biased estimates which do well under \(M_ 0\) at a small price in robustness. Extensions to confidence intervals, simultaneous estimation of several parameters and large sample approximations applying to nested parametric models are also discussed.
Reviewer: H.Büning

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62F10 Point estimation
62F25 Parametric tolerance and confidence regions
Full Text: DOI