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Abstract:

This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A restricted type of differentiability, called weak differentiability, is defined, which suffices to prove the asymptotic normality of estimates based on the functionals. This approach allows to prove the consistency, asymptotic normality and qualitative robustness of M estimates under more general conditions than those required in standard approaches. In particular, we prove that regression MMestimates are asymptotically normal when the observations are φ-mixing. © 2012 ISI/BS.

Registro:

Documento: Artículo
Título:Continuity and differentiability of regression M functionals
Autor:Fasano, M.V.; Maronna, R.A.; Sued, M.; Yohai, V.J.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, Calles 50 y 115, 1900 La Plata, Argentina
Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, 1426 Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 2, 1426 Buenos Aires, Argentina
Palabras clave:Asymptotic normality; Consistency; MM estimates; Nonlinear regression; S estimates
Año:2012
Volumen:18
Número:4
Página de inicio:1284
Página de fin:1309
DOI: http://dx.doi.org/10.3150/11-BEJ368
Título revista:Bernoulli
Título revista abreviado:Bernoulli
ISSN:13507265
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13507265_v18_n4_p1284_Fasano

Referencias:

  • Bianco, A.M., Yohai, V.J., Robust estimation in the logistic regression model (1996) Robust Statistics, Data Analysis, and Computer Intensive Methods, 109, pp. 17-34. , (Schloss Thurnau, 1994) (H. Rieder, ed.). Lecture Notes in Statist. New York: Springer. MR1491394
  • Billingsley, P., (1968) Convergence of Probability Measures, , New York: Wiley. MR0233396
  • Boos, D.D., Serfling, R.J., A note on differentials and the CLT and LIL for statistical functions, with application to M-estimates (1980) Ann. Statist., 8, pp. 618-624. , MR0568724
  • Čížek, P., Least trimmed squares in nonlinear regression under dependence (2006) J. Statist. Plann. Inference, 136, pp. 3967-3988. , MR2299174
  • Clarke, B.R., Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations (1983) Ann. Statist., 11, pp. 1196-1205. , MR0720264
  • Clarke, B.R., A remark on robustness and weak continuity of M-estimators (2000) J. Austral. Math. Soc. Ser. A, 68, pp. 411-418. , MR1753369
  • Croux, C., Dhaene, G., Hoorelbeke, D., Robust standard errors for robust estimators (2003) Discussions Paper Series (DPS) 03.16, , http://www.econ.kuleuven.be/ew/academic/econmetr/members/dhaene/papers/ rsejan2004.pdf, Center for Economic Studies, Katholieke Universiteit Leuven
  • Croux, C., Haesbroeck, G., Implementing the Bianco and Yohai estimator for logistic regression (2003) Comput. Statist. Data Anal., 44, pp. 273-295. , MR2020151
  • Doukhan, P., Mixing: Properties and examples (1994) Lecture Notes in Statistics, 85. , New York: Springer. MR1312160
  • Fasano, M.V., (2009) Robust Estimation in Nonlinear Regression., , http://www.mate.unlp.edu.ar/tesis/tesis_fasano_v.pdf, Ph.D. thesis, Univ. La Plata
  • Fernholz, L.T., Von mises calculus for statistical functionals (1983) Lecture Notes in Statistics, 19. , New York: Springer MR0713611
  • Fraiman, R., General M-estimators and applications to bounded influence estimation for nonlinear regression (1983) Comm. Statist. Theory Methods, 12, pp. 2617-2631. , MR0715170
  • Hampel, F.R., A general qualitative definition of robustness (1971) Ann. Math. Statist., 42, pp. 1887-1896. , MR0301858
  • Hampel, F.R., The influence curve and its role in robust estimation (1974) J. Amer. Statist. Assoc., 69, pp. 383-393. , MR0362657
  • Ibragimov, I.A., On the composition of unimodal distributions (1956) Theory Probab. Appl., 1, pp. 255-260
  • Kudraszow, N.L., Maronna, R.A., Estimates of MM type for the multivariate linear model (2011) J. Multivariate Anal., 102, pp. 1280-1292
  • Liese, F., Vajda, I., A general asymptotic theory of M-estimators. i (2003) Math. Methods Statist., 12, pp. 454-477. , MR2054158
  • Liese, F., Vajda, I., A general asymptotic theory of M-estimators. II (2004) Math. Methods Statist., 13, pp. 82-95. , MR2078314
  • Maronna, R.A., Martin, R.D., Yohai, V.J., Robust statistics: Theory and methods (2006) Wiley Series in Probability and Statistics, , Chichester: Wiley. MR2238141
  • Mizera, I., On consistent M-estimators: Tuning constants, unimodality and breakdown (1994) Kybernetika (Prague), 30, pp. 289-300. , MR1291931
  • Papantoni-Kazakos, P., Gray, R.M., Robustness of estimators on stationary observations (1979) Ann. Probab., 7, pp. 989-1002. , MR0548893
  • Rousseeuw, P., Yohai, V., Robust regression by means of S-estimators (1984) Lecture Notes in Statist., 26, pp. 256-272. , Robust and Nonlinear Time Series Analysis (Heidelberg, 1983) (J. Franke, W. Härdle and R.D. Martin, eds.) New York: Springer. MR0786313
  • Sakata, S., White, H., S-estimation of nonlinear regression models with dependent and heterogeneous observations (2001) J. Econometrics, 103, pp. 5-72. , Studies in estimation and testing. MR1838195
  • Stromberg, A.J., Consistency of the least median of squares estimator in nonlinear regression (1995) Comm. Statist. Theory Methods, 24, pp. 1971-1984. , MR1345230
  • Sued, M., Yohai, V.J., (2010) Robust Location Estimates with Missing Data., , Available at ArXiv:1004.5418v2 [math.ST]
  • Vǎiner, B.P., Kukush, O.G., The consistency of M-estimators constructed from a concave weight function (1998) Theory Probab. Math. Stat., 57, pp. 11-18
  • Yohai, V.J., High breakdown point and high efficiency robust estimates for regression (1985) Technical Report 66, , http://www.stat.washington.edu/research/reports/1985/tr066.pdf, Dept. Statistics, Univ. Washington
  • Yohai, V.J., High breakdown-point and high efficiency robust estimates for regression (1987) Ann. Statist., 15, pp. 642-656. , MR0888431

Citas:

---------- APA ----------
Fasano, M.V., Maronna, R.A., Sued, M. & Yohai, V.J. (2012) . Continuity and differentiability of regression M functionals. Bernoulli, 18(4), 1284-1309.
http://dx.doi.org/10.3150/11-BEJ368
---------- CHICAGO ----------
Fasano, M.V., Maronna, R.A., Sued, M., Yohai, V.J. "Continuity and differentiability of regression M functionals" . Bernoulli 18, no. 4 (2012) : 1284-1309.
http://dx.doi.org/10.3150/11-BEJ368
---------- MLA ----------
Fasano, M.V., Maronna, R.A., Sued, M., Yohai, V.J. "Continuity and differentiability of regression M functionals" . Bernoulli, vol. 18, no. 4, 2012, pp. 1284-1309.
http://dx.doi.org/10.3150/11-BEJ368
---------- VANCOUVER ----------
Fasano, M.V., Maronna, R.A., Sued, M., Yohai, V.J. Continuity and differentiability of regression M functionals. Bernoulli. 2012;18(4):1284-1309.
http://dx.doi.org/10.3150/11-BEJ368