Agostinelli, Claudio Bias bound for the minimax estimator. (English) Zbl 1160.62015 J. Stat. Plann. Inference 139, No. 7, 2235-2241 (2009). Summary: The bias bound function of an estimator is an important quantity in order to perform globally robust inference. We show how to evaluate the exact bias bound for the minimax estimator of the location parameter for a wide class of unimodal symmetric location and scale families. We show, by an example, how to obtain an upper bound of the bias bound for a unimodal asymmetric location and scale family. We provide the exact bias bound of the minimum distance/disparity estimators under a contamination neighborhood generated from the same distance. MSC: 62F10 Point estimation 60E15 Inequalities; stochastic orderings 62C20 Minimax procedures in statistical decision theory Keywords:maximum bias; location-scale model; minimax estimator; minimum distance estimator Software:sn PDFBibTeX XMLCite \textit{C. Agostinelli}, J. Stat. Plann. Inference 139, No. 7, 2235--2241 (2009; Zbl 1160.62015) Full Text: DOI References: [1] Adrover, J.; Berrendero, J. R.; Salibian-Barrera, M.; Zamar, R. H., Globally robust inference, Estadistica, 54, 162, 163, 127-161 (2002) · Zbl 1034.62027 [2] Adrover, J.; Salibian-Barrera, M.; Zamar, R. H., Globally robust inference for the location and simple linear regression models, J. Statist. Plann. Inference, 119, 2, 353-375 (2004) · Zbl 1032.62027 [3] Agostinelli, C., 2007. Estimating the model of the majority of the data, Advances and Applications in Statistical Sciences, submitted for publication.; Agostinelli, C., 2007. Estimating the model of the majority of the data, Advances and Applications in Statistical Sciences, submitted for publication. · Zbl 1194.62023 [4] Agostinelli, C., 2008. Bounds for the bias of estimators under contamination, Sankya, submitted for publication.; Agostinelli, C., 2008. Bounds for the bias of estimators under contamination, Sankya, submitted for publication. [5] Azzalini, A., The skew-normal distribution and related multivariate families, Scand. J. Statist., 32, 159-188 (2005) · Zbl 1091.62046 [6] Berrendero, J. R.; Zamar, R. H., The maxbias curve of robust regression estimates, Ann. Statist., 29, 1, 224-251 (2001) · Zbl 1029.62028 [7] Donoho, D. L.; Liu, R. C., The “automatic” robustness of minimum distance estimators, Ann. Statist., 16, 2, 552-586 (1988) · Zbl 0684.62030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.