Redescending M-estimators in regression analysis, cluster analysis and image analysis
Discussiones Mathematicae Probability and Statistics (2004)
- Volume: 24, Issue: 1, page 59-75
- ISSN: 1509-9423
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] D.F. Andrews, P.J. Bickel, F.R. Hampel, P.J. Huber, W.H. Rogers and J.W. Tukey, Robust Estimates of Location. Survey and Advances, Princeton University Press, Princeton 1972. Zbl0254.62001
- [2] O. Arslan, A simple test to identify good solutions of redescending M estimating equations for regression, Developments in Robust Statistics, Proceedings of ICORS 2001, R. Dutter, U. Gather, P.J. Rousseeuw and P. Filzmoser, (Eds.), (2003), 50-61. Zbl1135.62351
- [3] T. Bednarski and Ch.H. Müller, Optimal bounded influence regression and scale M-estimators, Statistics 35 (2001), 349-369. Zbl0995.62028
- [4] P.J. Bickel, Quelque aspects de la statistique robuste, In École d'Été de Probabilités de St. Flour. Springer Lecture Notes in Math. 876 (1981), 1-72.
- [5] P.J. Bickel, Robust regression based on infinitesimal neighbourhoods, Ann. Statist. 12 (1984), 1349-1368. Zbl0567.62051
- [6] H. Chen and P. Meer, Robust computer vision through kernel density estimation, ECCV 2002, LNCS 2350, A. Heyden et al. (Eds.), Springer, Berlin (2002), 236-250. Zbl1034.68586
- [7] H. Chen, P. Meer and D.E. Tyler, Robust regression for data with multiple structures, 2001 IEEE Conference on Computer Vision and Pattern Recognition, vol. I, Kauai, HI, (2001), 1069-1075.
- [8] C.K. Chu, I.K. Glad, F. Godtliebsen and J.S. Marron, Edge-preserving smoothers for image processing, J. Amer. Statist. Assoc. 93, (1998), 526-541. Zbl0954.62115
- [9] B.R. Clarke, Uniqueness and Frechét differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 4 (1983), 1196-1205. Zbl0541.62023
- [10] B.R. Clarke, Asymptotic theory for description of regions in which Newton-Raphson iterations converge to location M-estimators, J. Statist. Plann. Inference 15 (1986), 71-85. Zbl0657.62049
- [11] J.R. Collins, Robust estimation of a location parameter in the presence of asymmetry, Ann. Statist. 4 (1976), 68-85. Zbl0351.62035
- [12] J.B. Copas, On the unimodality of the likelihood for the Cauchy distribution, Biometrika 62 (1975), 701-704. Zbl0321.62037
- [13] D.L. Donoho. and J.P. Huber, The notion of breakdown point, P.J. Bickel, K.A. Doksum and J.L. Hodges, Jr., Eds., A Festschrift for Erich L. Lehmann, Wadsworth, Belmont, CA, (1983), 157-184.
- [14] S.P. Ellis and S. Morgenthaler, Leverage and breakdown in L1 regression, J. Amer. Statist. Assoc. 87 (1992), 143-148. Zbl0781.62101
- [15] D.A. Freedman and P. Diaconis, On inconsistent M-estimators, Ann. Statist. 10 (1982), 454-461. Zbl0496.62034
- [16] G. Gabrielsen, On the unimodality of the likelihood for the Cauchy distribution: Some comments, Biometrika 69 (1982), 677-678. Zbl0499.62031
- [17] F.R. Hampel, Optimally bounding the gross-error-sensitivity and the influence of position in factor space, Proceedings of the ASA Statistical Computing Section, ASA, Washington, D.C., (1978), 59-64.
- [18] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics - The Approach Based on Influence Functions, John Wiley, New York 1986. Zbl0593.62027
- [19] W. Härdle and T. Gasser, Robust nonparametric function fitting, J. R. Statist. Soc. B 46 (1984), 42-51. Zbl0543.62034
- [20] X. He, J. Jurecková, R. Koenker and S. Portnoy, Tail behavior of regression estimators and their breakdown points, Econometrica 58 (1990), 1195-1214. Zbl0745.62030
- [21] X. He, D.G. Simpson and G. Wang, Breakdown points of t-type regression estimators, Biometrika 87 (2000), 675-687. Zbl1120.62320
- [22] C. Hennig, Regression fixed point clusters: motivation, consistency and simulations, Preprint 2000-02, Fachbereich Mathematik, Universität Hamburg 2000.
- [23] C. Hennig, Clusters, outliers, and regression: Fixed point clusters, Journal of Multivariate Analysis. 86/1 (2003), 183-212. Zbl1020.62051
- [24] M. Hillebrand, On robust corner-preserving smoothing in image processing, Ph.D. thesis at the Carl von Ossietzky University Oldenburg, Germany 2002.
- [25] M. Hillebrand and Ch.H. Müller, On consistency of redescending M-kernel smoothers, Submitted 2002.
- [26] P.J. Huber, Minimax aspects of bounded-influence regression (with discussion), J. Amer. Statist. Assoc. 78 (1983), 66-80. Zbl0514.62073
- [27] J. Jurecková and P.K. Sen, Robust Statistical Procedures. Asymptotics and Interrelations, Wiley, New York 1996. Zbl0862.62032
- [28] W.S. Krasker, Estimation in linear regression models with disparate data points, Econometrica 48 (1980), 1333-1346. Zbl0467.62096
- [29] V. Kurotschka and Ch.H. Müller, Optimum robust estimation of linear aspects in conditionally contaminated linear models, Ann. Statist. 20 (1992), 331-350. Zbl0792.62024
- [30] K.L. Lange, R.J.A. Little and J.M.G. Taylor, Robust statistical modeling using the t distribution J. Amer. Statist. Assoc. 84 (1989), 881-896.
- [31] R.A. Maronna, O.H. Bustos and V.J. Yohai, Bias- and efficiency-robustness of general M-estimators for regression with random carriers, Smoothing Techniques for Curve Estimation (T. Gasser and M. Rosenblatt, eds.) Springer, Berlin, Lecture Notes in Mathematics 757 (1979), 91-116. Zbl0416.62050
- [32] I. Mizera, On consistent M-estimators: tuning constants, unimodality and breakdown, Kybernetika 30 (1994), 289-300. Zbl0815.62013
- [33] I. Mizera, Weak continuity of redescending M-estimators of location with an unbounded objective function, Tatra Mountains Math. Publ. 7 (1996), 343-347. Zbl0919.62024
- [34] I. Mizera and Ch.H. Müller, Breakdown points and variation exponents of robust M-estimators in linear models, Ann. Statist. 27 (1999), 1164-1177. Zbl0959.62029
- [35] I. Mizera and Ch.H. Müller, Breakdown points of Cauchy regression-scaleestimators, Stat. & Prob. Letters 57 (2002), 79-89. Zbl1039.62025
- [36] S. Morgenthaler, Fitting redescending M-estimators in regression, Robust Regression, H.D. Lawrence and S. Arthur, (Eds.), Dekker, New York (1990), 105-128. Zbl0719.62081
- [37] Ch.H. Müller, Optimal designs for robust estimation in conditionally contaminated linear models, J. Statist. Plann. Inference. 38 (1994), 125-140. Zbl0803.62066
- [38] Ch.H. Müller, Breakdown points for designed experiments, J. Statist. Plann. Inference, 45 (1995), 413-427. Zbl0827.62066
- [39] Ch.H. Müller, Optimal breakdown point maximizing designs, Tatra Mountains Math. Publ. 7, (1996), 79-85. Zbl0920.62093
- [40] Ch.H. Müller, Robust Planning and Analysis of Experiments, Springer, New York, Lecture Notes in Statistics 124 (1997).
- [41] Ch.H. Müller, On the use of high breakdown point estimators in the image analysis, Tatra Mountains Math. Publ. 17 (1999), 283-293. Zbl1067.62546
- [42] Ch.H. Müller, Robust estimators for estimating discontinuous functions, Metrika 55 (2002a), 99-109. Zbl1320.62077
- [43] Ch.H. Müller, Comparison of high-breakdown-point estimators for image denoising, Allg. Stat. Archiv 86 (2002b), 307-321. Zbl1123.62310
- [44] Ch.H. Müller and T. Garlipp, Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images, To appear in Journal of Multivariate Analysis, (2002). Zbl1062.62114
- [45] P. Qiu, Nonparametric estimation of jump surface, The Indian Journal of Statistics 59, Series A, (1997), 268-294. Zbl0886.62046
- [46] H. Rieder, Robust regression estimators and their least favorable contamination curves, Stat. Decis. 5 (1987), 307-336. Zbl0631.62035
- [47] H. Rieder, Robust Asymptotic Statistics, Springer, New York 1994.
- [48] B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London 1986. Zbl0617.62042
- [49] S. Smith and J. Brady, SUSAN - a new approach to low level image processing, International Journal of Computer Vision 23 (1997), 45-78.
- [50] R.H. Zamar, Robust estimation in the errors-in-variables model, Biometrika 76 (1989), 149-160. Zbl0664.62030