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Sequential Analysis
Design Methods and Applications
Volume 14, 1995 - Issue 3
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Original Articles

The asymptotics for studentized K-Step M-Estimators of location

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Pages 229-245 | Published online: 29 Mar 2007

References

  • Andrews , D.F. , Bickel , P.J. , Hampel , F.R. , Huber , P.J. , Rogers , W.H. and Tukey , J.W. 1972 . Robust Estimates of Location. Survey and Advances , Princeton Univ.Press .
  • Bickel , P.J. 1973 . Analogues of linear combinations of order statistics in the general linear model . Ann. Statist , 1 : 597 – 616 .
  • Bickel , P.J. 1975 . One-step Huber estimates in the linear model . J.Amer.Statist. Assoc , 70 : 428 – 433 .
  • Csöröo , M. and Révész , P. 1981 . “ Strong Approximations in Probability and Statistics ” . In Akadémiai Kiadó Budapest
  • Davies , P.L . 1992 . An efficient Frechet differentiate high breakdown multivariate location and dispersion estimator . J.Multiv. Analysis Statist. Assoc , 40 : 311 – 327 .
  • Field , C.A. and Wiens , D.P. 1994 . One-step M-estimator in the linear model with dependent errors . Canad. J. Statist , 22 : 219 – 231 .
  • Freedman , D. and Diaconis , P. 1982 . On inconsistent M-estimators . Ann. Statist , 10 : 454 – 461 .
  • Hampel , F.R. , Rousseeuw , P.J. , Ronchetti , E.M. and Stahel , W.A. 1986 . “ Robust Statistics ” . In The Approach Based on Influence Functions , New York : J. Wiley .
  • Huber , P.J. 1981 . Robust Statistics , New York : J. Wiley .
  • Janssen , P. , Jurečková , J. and Veraverbeke , N. 1985 . Rate of convergence of one- and two-step M-estimators with applications to maximum likelihood and pitman estimators . Ann. Stat. , 13 : 1222 – 1229 .
  • 1980 . Asymptotic representation of M-estimators of location . Operationsforschung und Statistik Ser statistics , 11 : 61 – 73 .
  • . Robust estimators of location and regression parameters and their second order asymptotic relations . Trans. 9th Prague Conf. on Inform. Theory, Statist. Decis. Functions and Random Processes . Dordrecht, Reidel. pp. 19 – 32 .
  • 1985 . Representation of M-estimators with the second order asymptotic distribution . Statistics & Decisions , 3 : 263 – 276 .
  • 1986 . Asymptotic representation of L-estimators and their relations to M-estimators . Sequential Analysis , A 16 : 317 – 338 .
  • 1987 . Asymptotics for one-step M-estimators in regression with application to combining high efficiency and high breakdown point . Commun. Statist , A 16 : 2187 – 2199 .
  • 1989 . Uniform second order asymptotic linarity of M-statistics in linear models . Statistics & Decisions , 7 : 263 – 276 .
  • 1990 . Effect of the initial estimator on the asympotic behavior of one-step M-estimator . Ann. Statistics Math. , 42 : 345 – 357 .
  • 1995 . “ Robust Statistical Procedures ” . In Asymptotics and Inter-Relations , J. Wiley . (in print)
  • Jurečková , J. 1990 . Asymptotic relations between L- and M- estimators in the linear model . Ann. Statistics Math. , 42 : 671 – 698 .
  • 1975 . An approximation of partial sums of independent RV's, and the sample DF I . Z. Wahrschein-lichkeitsth , 32 : 111 – 131 .
  • Malý M. Studentized M-estimators and their k-step versions (in Czech) Charles University Prague 1991 PhD Thesis
  • Müller C. One-step M-estimators in conditionally contaminated linear models Freie Universität Berlin 1992 Preprint A-92-11
  • Rousseuw , P.J. and Croux , C. 1994 . The bias of fc-step M-estimators . Statist. Probab. Letters , 20 : 411 – 420 .
  • Ruppert , D. and Carroll , R.J. 1980 . Trimmed least squares estimation in the linear model . J. Amer. Statist. Assoc , 75 : 828 – 838 .
  • Simpson , D.G. , Ruppert , D. and Carroll , R.J. 1992 . On the one step GM-estimates and stability of inferences in linear regression . J.Amer. Statist. Assoc , 87 : 439 – 450 .

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