Bickel, P. J. Parametric robustness: Small biases can be worthwhile. (English) Zbl 0545.62028 Ann. Stat. 12, 864-879 (1984). 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 Cited in 2 ReviewsCited in 18 Documents MSC: 62F35 Robustness and adaptive procedures (parametric inference) 62F10 Point estimation 62F25 Parametric tolerance and confidence regions Keywords:pretesting; limited translation estimates; Gaussian linear model; maximum risk; least square estimate; robustness; biased estimates; simultaneous estimation; large sample approximations; nested parametric models × Cite Format Result Cite Review PDF Full Text: DOI