Journal of the Korean Statistical Society

  • 제26권1호
  • /
  • Pages.1-22
  • /
  • 1997
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

A Study on a One-step Pairwise GM-estimator in Linear Models

  • Song, Moon-Sup (Department of Statistics, Seoul National University, Seoul, 151-742) ;
  • Kim, Jin-Ho (Korea Research Institute of Standards and Science, Taejon, 305-606)
  • 발행 : 1997.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

키워드

참고문헌

  1. Technometric v.16 A Robust Method for Multiple Linear Regression Andrew, D.F.
  2. Journal of the American Statistical Association v.70 One-Step Huber Estimates in the Linear Model Bickel, P.J.
  3. Journal of the American Statistical Association v.88 A Bounded Influence, High Breakdown, Efficient Regression Estimator Coakley, C.W.;Hettmansperger, T.P.
  4. Journals of the American Statistical Association v.84 Mallows-Type Bounded-Influence Trimmed Means De Jongh, P.J.;De Wet, T.;Welsh, T.P.
  5. In A Festschrift for Erich Lehmann The Notion of Breakdowm Point Donoho, D.L.;Huber, P.J.;P. Bickel(ed.);K. Doksum(ed.);J.L. Hodges(ed.)
  6. Annals of Mathmatical Statistics v.42 A General Qualitative Definition of Robustness Hampel, F.R.
  7. Journal of the American Statistical Association v.69 The Influence Curve and Its Role in Robust Estimation Hampel, F.R.
  8. Psychometrica v.43 Statistical Inference Based on Ranks Hettmansperger, T.P.;McKean, J.W.
  9. The Annals of Statistics v.1 Robust Regression: Asymtotics, Conjectures, and Monte Carlo Huber, P.J.
  10. Annals of Mathmetical Statistics v.43 Estimation Regression Coefficients by Minimizing the Despersion of the Residuals Jaeckel, L.A.
  11. Theory and Methods v.16 no.8 Asymtotics for One-Step M-Estimators in Regression with Application to Combining Efficiency and High Breakdown Point, Communications in Statistics, Jurekova, J.;Portnoy, S.
  12. Journal of the American Statistical Association v.77 Efficient Bounded-Influence Regression Estimation Krasker, W.S.;Welsch, R.E.
  13. U-statistics Theory and Practice Lee, A.J.
  14. Zeitschrift fur Wahrscheinlichkeitsytheoriw und verwandte Gebiete v.58 Asymptotic Behavior of General M-estimates for Regression and Scale with Random Carriers Maronna, R.A.;Yohai, V.J.
  15. Journal of Royal Statistical Society, Series B v.56 no.1 Bounded Influence Rank Regression Naranjo, J.D.;Hettmansperger, T.P.
  16. Robust Regressiopn and Outlier Detection Rousseeuw, P.J.;Leroy, A.M.
  17. Journal of the American Statistical Association v.79 Least Median of Squares Regression Rousseeuw, P.J.
  18. In Robust and Nonlinear Time Series;Lectures Notes in Statistics No. 26 Robust Regression by Means of S-Estimators Rousseeuw, P.J.;Yohai, V.;J. Franke(ed.);W. Hardle(ed.);R.D. Martin(ed.)
  19. Communication in Statistics - Theory and Methods v.12 no.10 A Weighted Dispersion Function for Estimation in Linear Models Sievers, G.L.
  20. Journal of the American Statistical Association v.87 On One-Step GM Estimates and Stability of Inferences in Linear Regression Simpson, D.G.;Ruppert, D.;Carroll, R.J.
  21. Journal of the Korean Statistical Society, in Proceeding A High Breakdowm and Efficient GM-Estimator in Linear Models Song, M.S.;Park, Ch. S.;Nam, H.S.
  22. S-PLUS for Windows User's Manual Statistical Sciences
  23. Journal of the American Statistical Association v.83 High Breandowm Point Estimates of Regression by Means of the Minimization of an Efficient Scale Yohai, V.J.;Zamar, R.H.