Maronna, Ricardo A.; Yohai, Victor J. Bias-robust estimates of regression based on projections. (English) Zbl 0787.62037 Ann. Stat. 21, No. 2, 965-990 (1993). The authors introduce a new class of regression estimators which are based on (univariate) regressions of the response variable with respect to all one-dimensional projections of the carriers. They are called projection estimators \((P\)-estimators). \(P\)-estimators are regression, affine and scale equivariant and are shown to have a ratio of consistency of \(\sqrt n\). These estimators are highly bias-robust and possess both bounded influence and high breakdown point.Numerical computations of the asymptotic bias and Monte Carlo estimations of the mean squared error under contamination for finite sample sizes show that \(P\)-estimators compare very favourably with other robust estimators. Reviewer: H.Büning (Berlin) Cited in 2 ReviewsCited in 18 Documents MSC: 62F35 Robustness and adaptive procedures (parametric inference) 62J05 Linear regression; mixed models Keywords:minimax bias; \(P\)-estimators; new class of regression estimators; projection estimators; scale equivariant; consistency; bias-robust; bounded influence; high breakdown point; asymptotic bias; Monte Carlo estimations; mean squared error; contamination; finite sample sizes; robust estimators PDFBibTeX XMLCite \textit{R. A. Maronna} and \textit{V. J. Yohai}, Ann. Stat. 21, No. 2, 965--990 (1993; Zbl 0787.62037) Full Text: DOI