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Original Articles

Some maximum-indifference estimators for the slope of a univariate linear model

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Pages 395-412 | Received 27 Dec 2014, Accepted 03 Jan 2016, Published online: 08 Apr 2016

References

  • Akritas, M.G., Murphy, S.A., and Lavalley, M.P. (1995), ‘The Theil–Sen Estimator with Doubly Censored Data and Applications to Astronomy’, Journal of the American Statistical Association, 90, 170–177. doi: 10.1080/01621459.1995.10476499
  • Andrews, D.F. (1974), ‘A Robust Method for Multiple Linear Regression’, Technometrics, 16, 523–531. doi: 10.1080/00401706.1974.10489233
  • Birkes, D., and Dodge, Y. (1993), Alternative Methods of Regression, New York: John Wiley & Sons.
  • Borroni, C.G. (2013), ‘A New Rank Correlation Measure’, Statistical Papers, 54, 255–270. doi: 10.1007/s00362-011-0423-0
  • Borroni, C.G., and Zenga, M. (2007), ‘A Test of Concordance Based on Gini's Mean Difference’, Statistical Methods & Applications, 16, 289–308. doi: 10.1007/s10260-006-0037-1
  • Chatterjee, S., and Olkin, I. (2006), ‘Nonparametric Estimation for Quadratic Regression’, Statistics & Probability Letters, 76, 1156–1163. doi: 10.1016/j.spl.2005.12.022
  • Cifarelli, D.M. (1978), ‘La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini’, Rivista di matematica per le scienze economiche e sociali, A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance, 1, 7–38.
  • Cifarelli, D.M., Conti, P.L., and Regazzini, E. (1996), ‘On the Asymptotic Distribution of a General Measure of Monotone Dependence’, Annals of Statistics, 24, 1386–1399. doi: 10.1214/aos/1032526975
  • Cifarelli, D.M., and Regazzini, E. (1990), ‘Some Contribution to the Theory of Monotone Dependence’, Technical Report 90.17, CNR-IAMI, Milano.
  • Fernandes, R., and Leblanc, S.G. (2005), ‘Parametric (Modified Least Squares) and Non-parametric (Theil–Sen) Linear Regressions for Predicting Biophysical Parameters in the Presence of Measurement Errors’, Remote Sensing of Environment, 95, 303–316. doi: 10.1016/j.rse.2005.01.005
  • Genest, C., Nešlehová, J., and Ben Ghorbal, N. (2010), ‘Spearman's Footrule and Gini's Gamma: A Review with Complements’, Journal of Nonparametric Statistics, 22, 937–954. doi: 10.1080/10485250903499667
  • Gini, C. (1912), Variabilità e Mutabilità; Contributo allo Studio delle Distribuzioni e Relazioni Statistiche, Regia Università di Cagliari.
  • Gini, C. (1954), Corso di Statistica, Rome: Veschi.
  • Hájek, J., Šidák, Z., and Sen, P.K. (1999), Theory of Rank Tests (2nd ed.), San Diego, CA: Academic Press.
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: John Wiley & Sons.
  • Koenker, R., and Bassett Jr., G. (1980), ‘Regression Quantiles’, Econometrica, 46, 33–50. doi: 10.2307/1913643
  • Peng, H., Wang, S., and Wang, X. (2008), ‘Consistency and Asymptotic Distribution of the Theil–Sen Estimator’, Journal of Statistical Planning and Inference, 138, 1836–1850. doi: 10.1016/j.jspi.2007.06.036
  • Rousseeuw, P.J., and Leroy, A.M. (1987), Robust Regression and Outlier Detection, New York: John Wiley & Sons.
  • Ruppert, D., and Carroll, R.J. (1980), ‘Trimmed Least Squares Estimation in the Linear Model’, Journal of the American Statistical Association, 75, 828–838. doi: 10.1080/01621459.1980.10477560
  • Sen, P.K. (1968), ‘Estimates of the Regression Coefficient Based on Kendall's Tau’, Journal of the American Statistical Association, 63, 1379–1389. doi: 10.1080/01621459.1968.10480934
  • Sen, P.K. (2011), ‘The Theil–Sen Estimator in Genomic High Dimensional Measurement Error Models Perspectives’, Calcutta Statistical Association Bulletin, 63, 37–50.
  • Shirahata, S., and Wakimoto, K. (1984), ‘Asymptotic Normality of a Class of Nonlinear Rank Tests for Independence’, Annals of Statistics, 12, 1124–1129. doi: 10.1214/aos/1176346730
  • Siegel, A.F. (1982), ‘Robust Regression Using Repeated Medians’, Biometrika, 69, 242–244. doi: 10.1093/biomet/69.1.242
  • Theil, H. (1950), ‘A Rank Invariant Method of Linear and Polynomial Regression Analysis, I, II, III’, Proceedings of the Koninklijke Nederlandse Akademie Wetenschappen, Series A – Mathematical Sciences, 53, 386–392, 521–525, 1397–1412.
  • Wang, X., and Yu, Q. (2005), ‘Unbiasedness of the Theil–Sen Estimator’, Journal of Nonparametric Statistics, 17, 685–695. doi: 10.1080/10485250500039452
  • Wilcox, R. (1998), ‘A Note on the Theil–Sen Regression Estimator When the Regressor Is Random and the Error Term Is Heteroscedastic’, Biometrical Journal, 40, 261–268. doi: 10.1002/(SICI)1521-4036(199807)40:3<261::AID-BIMJ261>3.0.CO;2-V
  • Zhou, W., and Serfling, R. (2008), ‘Multivariate Spatial U-Quantiles: A Bahadur-Kiefer Representation, a Theil–Sen Estimator for Multiple Regression, and a Robust Dispersion Estimator’, Journal of Statistical Planning and Inference, 138, 1660–1678. doi: 10.1016/j.jspi.2007.05.043

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