Navegar

Colección

Datos Estadísticas

Artículo

Ferretti, N.; Kelmansky, D.; Yohai, V.J.; Zamar, R.H. "A Class of Locally and Globally Robust Regression Estimates" (1999) Journal of the American Statistical Association. 94(445):174-188
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We recommend, however, choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step. The generalized τ estimate with loss functions ρ1 and ρ2 is related to the Hill–Ryan GM estimate with a loss function ρ, which is a linear combination of ρ1 and ρr. In fact, both estimates have the same influence function and asymptotic distribution under the central model. We show that a certain generalized τ estimate has good maximum bias behavior and performs well in an extensive Monte Carlo simulation study and three numerical examples. © 1999 Taylor & Francis Group, LLC.

Registro:

Documento: Artículo
Título:A Class of Locally and Globally Robust Regression Estimates
Autor:Ferretti, N.; Kelmansky, D.; Yohai, V.J.; Zamar, R.H.
Filiación:Department of Mathematics, National University of La Plata, Buenos Aires, Argentina
Institute of Calculus, University of Buenos Aires, 1428, Argentina
Department of Mathematics, University of Buenos Aires, 1428, Argentina
Department of Statistics, University of British Columbia, Vancouver, BC, V6T 17L, Canada
Palabras clave:Bounded influence; Breakdown point; Maximum bias; Robust regression
Año:1999
Volumen:94
Número:445
Página de inicio:174
Página de fin:188
DOI: http://dx.doi.org/10.1080/01621459.1999.10473834
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v94_n445_p174_Ferretti

Referencias:

  • Carroll, R.J., Ruppert, D., Transformations in regression. A robust analysis (1985) Technometrics, 27, pp. 1-12
  • Coakley, C.W., Hettmansperger, T.P., A bounded influence, high-breakdown, efficient regression estimator (1993) Journal of the American Statistical Association, 88, pp. 872-880
  • Donoho, D.L., (1982) Breakdown Properties of Multivariate Location Estimators, , Ph.D. qualifying paper, Harvard University
  • Ferretti, N., Kelmansky, D., Yohai, V.J., Zamar, R.H., (1996) Generalized R Estimates, , Technical Report 164, University of British Columbia, Dept, of Statistics
  • Hampel, F.R., A general qualitative definition of robustness (1971) Annals of Mathematical Statistics, 42, pp. 1887-1896
  • Hampel, F.R., The influence function and its role in robust estimation (1974) Journal of the American Statistical Association, 69, pp. 383-393
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust Statistics: The Approach Based on Influence Functions, , New York: Wiley
  • Hawkins, D.M., Simonoff, J.S., Stromberg, A.J., Distributing a computationally intensive estimator: The case of exact lms regression (1994) Computational Statistics, 9, pp. 83-95
  • He, X., A local breakdown property of robust tests in linear regression (1991) Journal of Multivariate Analysis, 38, pp. 294-305
  • He, X., Simpson, D.G., Robust direction estimation (1992) The Annals of Statistics, 20, pp. 351-369
  • He, X., Simpson, D.G., Lower bounds for contamination bias: Globally minimax versus locally linear estimation (1993) The Annals of Statistics, 21, pp. 314-337
  • Krasker, W.S., Estimation of a linear regression model with disparate data points (1980) Econometrica, 48, pp. 1333-1346
  • Krasker, W.S., Welsch, R.E., Efficient bounded influence regression estimation (1982) Journal of the American Statistical Association, 11, pp. 595-604
  • Maronna, R.A., Bustos, O.H., Yohai, V.J., Bias and efficiency robustness of general m-estimators for regression with random carries (1979) Smoothing Techniques for Curve Estimation, pp. 91-116. , Lecture Notes in Mathematics 757, eds. T. Gasser and M. Rosenblatt, Berlin: Springer
  • Maronna, R.A., Stahel, W.A., Yohai, V.J., Bias-robust estimators of multivariate scatter based on projections (1992) Journal of Multivariate Analysis, 42, pp. 141-161
  • Maronna, R.A., Yohai, V.J., Bias-robust estimates of regression based on projections (1993) The Annals of Statistics, 21, pp. 965-990
  • Maronna, R.A., Yohai, V.J., The behavior of the stahel-donoho robust multivariate estimator (1995) Journal of the American Statistical Association, 90, pp. 330-341
  • Martin, R.D., Yohai, V.J., Zamar, R.H., Min-max bias robust regression (1989) The Annals of Statistics, 17, pp. 1608-1630
  • Rousseeuw, P.J., Least median of squares regression (1984) Journal of the American Statistical Association, 79, pp. 871-880
  • Rousseeuw, P.J., A resampling design for computing high-breakdown regression (1993) Statistics and Probability Letters, 18, pp. 125-128
  • Rousseeuw, P.J., Leroy, A.M., (1987) Robust Regression and Outlier Detection, , New York: Wiley
  • Rousseeuw, P.J., Yohai, V.J., Robust regression by means of s estimators (1984) Robust and Nonlinear Time Series Analysis, pp. 256-272. , Lecture Notes in Statistics 26, eds. J. Franke, W. Härdle, and R. D. Martin, New York: Springer-Verlag
  • Ruppert, D., Carroll, R.J., Trimmed least squares estimation in the linear model (1980) Journal of the American Statistical Association, 75, pp. 828-838
  • Simpson, D.G., Ruppert, D., Carroll, R.J., On one-step gm estimates and stability of inferences in linear regression model (1992) Journal of the American Statistical Association, 87, pp. 439-450
  • Simpson, D.G., Yohai, V.J., Functional stability of one- step gm estimators in linear regression (1998) The Annals of Statistics, 26, pp. 1147-1169
  • Stahel, W.A., (1981) Robuste Schätzungen: Infinitesimale Optimalität Und Schätzungen Von Kovarianzmatrizen, , Ph.D. dissertation, Zürich: ETH
  • Stromberg, A.J., Computing the exact least median of squares estimate and stability diagnostics in multiple linear regression (1993) SIAM Journal on Scientific Computing, 14, pp. 1289-1299
  • Yohai, V.J., High-breakdown point and high-efficiency robust estimates for regression (1987) The Annals of Statistics, 15, pp. 642-656
  • Yohai, V.J., Zamar, R.H., High breakdown-point estimates of regression by means of the minimization of an efficient scale (1988) Journal of the American Statistical Association, 83, pp. 406-413
  • Yohai, V.J., Zamar, R.H., A minimax-bias property of the least alpha-quantile estimates (1993) The Annals of Statistics, 21, pp. 1824-1842
  • Yohai, V.J., Zamar, R.H., Optimal locally robust regression estimates (1997) Journal of Statistical Planning and Inference, 66, pp. 309-323

Citas:

---------- APA ----------
Ferretti, N., Kelmansky, D., Yohai, V.J. & Zamar, R.H. (1999) . A Class of Locally and Globally Robust Regression Estimates. Journal of the American Statistical Association, 94(445), 174-188.
http://dx.doi.org/10.1080/01621459.1999.10473834
---------- CHICAGO ----------
Ferretti, N., Kelmansky, D., Yohai, V.J., Zamar, R.H. "A Class of Locally and Globally Robust Regression Estimates" . Journal of the American Statistical Association 94, no. 445 (1999) : 174-188.
http://dx.doi.org/10.1080/01621459.1999.10473834
---------- MLA ----------
Ferretti, N., Kelmansky, D., Yohai, V.J., Zamar, R.H. "A Class of Locally and Globally Robust Regression Estimates" . Journal of the American Statistical Association, vol. 94, no. 445, 1999, pp. 174-188.
http://dx.doi.org/10.1080/01621459.1999.10473834
---------- VANCOUVER ----------
Ferretti, N., Kelmansky, D., Yohai, V.J., Zamar, R.H. A Class of Locally and Globally Robust Regression Estimates. J. Am. Stat. Assoc. 1999;94(445):174-188.
http://dx.doi.org/10.1080/01621459.1999.10473834