On Robust Estimation of Error Variance in (Highly) Robust Regression

[1] Hald A. (2006). A history of parametric statistical inference from Bernoulli to Fisher, 1713 to 1935. New York: Springer.Search in Google Scholar

[2] Dietrich, C.F. (1991). Uncertainty, calibration and probability. The statistics of scientific and industrial measurement. 2nd edn. Boca Raton: Taylor & Francis.Search in Google Scholar

[3] Neykov, N., Filzmoser, P., Dimova, R., & Neytchev, P. (2007). Robust fitting of mixtures using the trimmed likelihood estimator. Computational Statistics & Data Analysis, 52, 299–308.10.1016/j.csda.2006.12.024Search in Google Scholar

[4] White, G.H. (2008). Basics of estimating measurement uncertainty. Clinical Biochemist Reviews, 29, S53–S60.Search in Google Scholar

[5] Hekimoglu, S., Erenoglu, R.C., & Kalina, J. (2009). Outlier detection by means of robust regression estimators for use in engineering science. Journal of Zhejiang University Science A, 10, 909–921.10.1631/jzus.A0820140Search in Google Scholar

[6] Luukinen J.M., Aalto D., Malinen, J., Niikuni, N., Saunavaara, J., Jääsaari, P., Ojalammi. A., Parkkola, R., Soukka, T., & Happonen, R.P. (2018). A novel marker based method to teeth alignment in MRI. Measurement Science Review, 18, 79–85.10.1515/msr-2018-0012Search in Google Scholar

[7] Kumar, N., Hoque, M.A.,Shahjaman, M., Islam, S.M.S., Mollah, M.N.H. (2017). Metabolomic biomarker identification in presence of outliers and missing values. BioMed Research International, 2017, Article 2437608.10.1155/2017/2437608533116928293630Search in Google Scholar

[8] Kalina, J. (2018). A robust pre-processing of BeadChip microarray images. Biocybernetics and Biomedical Engineering, 38, 556–563.10.1016/j.bbe.2018.04.005Search in Google Scholar

[9] Jurečková, J., Picek, J., & Schindler, M. (2019). Robust statistical methods with R. 2nd edn. Boca Raton: CRC Press.10.1201/b21993Search in Google Scholar

[10] Rousseeuw, P.J. & Leroy, A.M. (1987). Robust regression and outlier detection. New York: Wiley.10.1002/0471725382Search in Google Scholar

[11] Kalina, J. (2012). Implicitly weighted methods in robust image analysis. Journal of Mathematical Imaging and Vision, 44, 449–462.10.1007/s10851-012-0337-zSearch in Google Scholar

[12] Víšek, J.Á. (2011). Consistency of the least weighted squares under heteroscedasticity. Kybernetika, 47, 179–206.Search in Google Scholar

[13] Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., & Stahel, W.A. (1986). Robust statistics. The approach based on influence functions. New York: Wiley.Search in Google Scholar

[14] Ranganai, E. (2016). On studentized residuals in the quantile regression framework. SpringerPlus, 5, Article 1231.10.1186/s40064-016-2898-6497100127536515Search in Google Scholar

[15] Davies, P.L. & Kovac A. (2001). Local extremes, runs, strings and multiresolution. Annals of Statistics, 29, 1–65.10.1214/aos/996986501Search in Google Scholar

[16] Rousseeuw, P.J. & Hubert, M. (2011). Robust statistics for outlier detection. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1, 73–79.10.1002/widm.2Search in Google Scholar

[17] Davies, L. (1990). The asymptotics of S-estimators in the linear regression model. Annals of Statistics, 18, 1651–1675.10.1214/aos/1176347871Search in Google Scholar

[18] Riani, M., Cerioli, A., & Torti, F. (2014). On consistency factors and efficiency of robust S-estimators. Test, 23, 356–387.10.1007/s11749-014-0357-7Search in Google Scholar

[19] Yohai, V.J. (1987). High breakdown-point and high efficiency robust estimates for regression. Annals of Statistics, 15, 642–656.10.1214/aos/1176350366Search in Google Scholar

[20] Víšek, J.Á. (2006). The least trimmed squares. Part I: Consistency. Kybernetika, 42, 1–36.Search in Google Scholar

[21] Roelant, E., Van Aelst, S., & Willems, G. (2009). The minimum weighted covariance determinant estimator. Metrika, 70, 177–204.10.1007/s00184-008-0186-3Search in Google Scholar

[22] Kalina, J. (2019). Common multivariate estimators of location and scatter capture the symmetry of the underlying distribution. Communications in Statistics—Simulation and Computation. In press.Search in Google Scholar

[23] Víšek, J.Á. (2010). Robust error-term-scale estimate. IMS Collections, 7, 254–267.10.1214/10-IMSCOLL725Search in Google Scholar

[24] Rousseeuw, P.J. & Van Driessen, K. (2006). Computing LTS regression for large data sets. Data Mining and Knowledge Discovery, 12, 29–45.10.1007/s10618-005-0024-4Search in Google Scholar

[25] Kalina, J. & Neoral, A. (2019). A robustified metalearning procedure for regression estimators. In Conference Proceedings, The 13th International Days of Statistics and Economics MSED 2019. Slaný: Melandrium, 617–726.10.18267/pr.2019.los.186.61Search in Google Scholar

[26] R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.Search in Google Scholar