Navegar

Colección

Datos Estadísticas

Artículo

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:

The classical Tukey–Huber contamination model (CCM) is a commonly adopted framework to describe the mechanism of outliers generation in robust statistics. Given a dataset with n observations and p variables, under the CCM, an outlier is a unit, even if only one or a few values are corrupted. Classical robust procedures were designed to cope with this type of outliers. Recently, a new mechanism of outlier generation was introduced, namely, the independent contamination model (ICM), where the occurrences that each cell of the data matrix is an outlier are independent events and have the same probability. ICM poses new challenges to robust statistics since the percentage of contaminated rows dramatically increase with p, often reaching more than 50% whereas classical affine equivariant robust procedures have a breakdown point of 50% at most. For ICM, we propose a new type of robust methods, namely, composite robust procedures that are inspired by the idea of composite likelihood, where low-dimension likelihood, very often the likelihood of pairs, are aggregated to obtain a tractable approximation of the full likelihood. Our composite robust procedures are built on pairs of observations to gain robustness in the ICM. We propose composite τ-estimators for linear mixed models. Composite τ-estimators are proved to have a high breakdown point both in the CCM and ICM. A Monte Carlo study shows that while classical S-estimators can only cope with outliers generated by the CCM, the estimators proposed here are resistant to both CCM and ICM outliers. Supplementary materials for this article are available online. © 2016 American Statistical Association.

Registro:

Documento: Artículo
Título:Composite Robust Estimators for Linear Mixed Models
Autor:Agostinelli, C.; Yohai, V.J.
Filiación:Dipartimento di Matematica, Università di Trento, Trento, Italy
Dipartimento di Scienze Ambientali, Informatica e Statistica, Universita' Ca' Foscari, Venezia, Italy
Facultad de Ciencias Exactas, Instituto de Cálculo, University of Buenos Aires, Buenos Aires, Argentina
Palabras clave:Composite τ-estimators; Independent contamination model; Robust estimation; Tukey–Huber contamination model
Año:2016
Volumen:111
Número:516
Página de inicio:1764
Página de fin:1774
DOI: http://dx.doi.org/10.1080/01621459.2015.1115358
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_v111_n516_p1764_Agostinelli

Referencias:

  • Alqallaf, F., Van Aelst, S., Zamar, R.H., Yohai, V.J., Propagation of Outliers in Multivariate Data (2009) The Annals of Statistics, 37, pp. 311-331
  • Anderson, D.K., Oti, R.S., Lord, C., Welch, K., Patterns of Growth in Adaptive Social Abilities Among Children With Autism Spectrum Disorders (2009) Journal of Abnormal Child Psychology, 37, pp. 1019-1034
  • Chervoneva, I., Vishnyakov, M., Constrained S-estimators for Linear Mixed Effects Models With Covariance Components (2011) Statistics in Medicine, 30, pp. 1735-1750
  • Copt, S., Heritier, S., (2006) MM-estimation and Inference in Mixed Linear Models, , Technical Report 2006.01, Faculté des Sciences Économiques et Sociales, Université de Genève
  • Copt, S., Victoria-Feser, M.P., High Breakdown Inference in the Mixed Linear Model (2006) Journal of American Statistical Association, 101, pp. 292-300
  • Davies, P.L., Asymptotic Behaviour of S-Estimates of Multivariate Location Parameters and Dispersion Matrices (1987) The Annals of Statistics, 15, pp. 1269-1292
  • Donoho, D.L., (1982) Breakdown Properties of Multivariate Location Estimators, , Qualifying Paper, Harvard University, Boston
  • Donoho, D.L., Huber, P.J., (1983) The Notion of Breakdown Point, , A Festschrift for Erich L. Lehmann, eds. P. J. Bickel, K. Doksum, and J. L. Hodges, Jr., Belmont, CA: Wadsworth, pp. 157--184
  • Fellner, W.H., Robust Estimation of Variance Components (1986) Technometrics, 28, pp. 51-60
  • Gill, P.S., A Robust Mixed Linear Model Analysis for Longitudinal Data (2000) Statistics in Medicine, 19, pp. 975-987
  • Hampel, F.R., A General Qualitative Definition of Robustness (1971) The Annals of Mathematical Statistics, 42, pp. 1887-1896
  • Heritier, S., Cantoni, E., Copt, S., Victoria-Feser, M.P., (2009) Robust methods in Biostatistics, , Chichester, UK: Wiley
  • Jacqmin-Gadda, H., Sibillot, S., Proust, C., Molina, J., Thiébaut, R., Robustness of the Linear Mixed Model to Misspecified Error Distribution (2007) Computational Statistics & Data Analysis, 51, pp. 5142-5154
  • Jiang, J., Zhang, W., Robust Estimation in Generalised Linear Mixed Models (2001) Biometrika, 88, pp. 753-765
  • Koller, M., (2013) Robust Estimation of Linear Mixed Models, , Ph.D. dissertation, ETH Zürich
  • Koller, M., (2015) robustlmm: Robust Linear Mixed Effects Models, , www.cran.r-project.org/web/packages/robustlmm/index.html
  • Lachosa, V.H., Deyb, D.K., Canchoc, V.G., Robust Linear Mixed Models With Skew-Normal Independent Distributions From a Bayesian Perspective (2009) Journal of Statistical Planning and Inference, 139, pp. 4098-4110
  • Lindsay, B.G., Composite Likelihood Methods (1988) Contemporary Mathematics, 80, pp. 221-239. , http://www.stat.psu.edu/ bgl/center/tr/PUB88a.pdf
  • Lopuhaä, H.P., Multivariate τ-estimators for Location and Scatter (1991) Canadian Journal of Statistics, 19, pp. 307-321
  • Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics. Theory and Methods, , Chichester, UK: Wiley
  • Muler, N., Yohai, V.J., Robust Estimators for ARCH Processes (2002) Journal of Time Series Analysis, 23, pp. 341-375
  • Papantoni-Kazakos, P., Gray, R.M., Robustness of Estimators on Stationary Observations (1979) The Annals of Probability, 7, pp. 989-1002
  • Richardson, A.M., Welsh, A.H., Robust Restricted Maximum Likelihood in Mixed Linear Models (1995) Biometrics, 51, pp. 1429-1439
  • Rocke, D.M., Robustness Properties of S-estimators of Multivariate Location and Shape in High Dimension (1996) The Annals of Statistics, 24, pp. 1327-1345
  • Rousseeuw, P., Multivariate Estimation With High Breakdown Point (1985) Mathematical Statistics and Applications, pp. 283-297. , Grossmann W., Pflug G., Vincze I., Wertz W., (eds), Dordrecht: Reidel Publishing Company (co-published with Akadémiai e Kiadó, Budapest)
  • Searle, S.R., Casella, G., McCulloch, C.E., (1992) Variance Components, , Hoboken, NJ: Wiley
  • Sinha, S.K., Robust Analysis of Generalized Linear Mixed Models (2004) Journal of the American Statistical Association, 99, pp. 451-460
  • Stahel, W.A., (1981) Robuste Schätzungen: Infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen, , Ph.D. dissertation, ETH Zürich
  • Stahel, W.A., Welsh, A.H., Approaches to Robust Estimation in the Simplest Variance Components Model (1997) Journal of Statistical Planning and Inference, 57, pp. 295-319
  • West, B.T., Welch, K.B., Galecki, A.T., (2007) Linear Mixed Models: A Practical Guide Using Statistical Software, , Boca Raton, FL: Chapman & Hall/CRC
  • 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. 413-460
  • Yohai, V.J., Optimal Locally Robust M-Estimates of Regression (1997) Journal of Statistical Planning and Inference, 64, pp. 309-323

Citas:

---------- APA ----------
Agostinelli, C. & Yohai, V.J. (2016) . Composite Robust Estimators for Linear Mixed Models. Journal of the American Statistical Association, 111(516), 1764-1774.
http://dx.doi.org/10.1080/01621459.2015.1115358
---------- CHICAGO ----------
Agostinelli, C., Yohai, V.J. "Composite Robust Estimators for Linear Mixed Models" . Journal of the American Statistical Association 111, no. 516 (2016) : 1764-1774.
http://dx.doi.org/10.1080/01621459.2015.1115358
---------- MLA ----------
Agostinelli, C., Yohai, V.J. "Composite Robust Estimators for Linear Mixed Models" . Journal of the American Statistical Association, vol. 111, no. 516, 2016, pp. 1764-1774.
http://dx.doi.org/10.1080/01621459.2015.1115358
---------- VANCOUVER ----------
Agostinelli, C., Yohai, V.J. Composite Robust Estimators for Linear Mixed Models. J. Am. Stat. Assoc. 2016;111(516):1764-1774.
http://dx.doi.org/10.1080/01621459.2015.1115358