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Additive regression models have a long history in multivariate non-parametric regression. They provide a model in which the regression function is decomposed as a sum of functions, each of them depending only on a single explanatory variable. The advantage of additive models over general non-parametric regression models is that they allow to obtain estimators converging at the optimal univariate rate avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integration is a common procedure to estimate each component in additive models. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated with the marginal integration procedure. The proposed estimators are consistent and asymptotically normally distributed. A simulation study allows to show the advantage of the proposal over the classical one when outliers are present in the responses, leading to estimators with good robustness and efficiency properties. © 2016, Sociedad de Estadística e Investigación Operativa.


Documento: Artículo
Título:Marginal integration M-estimators for additive models
Autor:Boente, G.; Martínez, A.
Filiación:Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Additive models; Kernel weights; Local M-estimation; Marginal integration; Robustness
Página de inicio:231
Página de fin:260
Título revista:Test
Título revista abreviado:Test


  • Alimadad, A., Salibián-Barrera, M., An outlier-robust fit for generalized additive models with applications to disease outbreak detection (2012) J Am Stat Assoc, 106, pp. 719-731
  • Baek, J., Wehrly, T., Kernel estimation for additive models under dependence (1993) Stoch Process Appl, 47, pp. 95-112
  • Bianco, A., Boente, G., Robust kernel estimators for additive models with dependent observations (1998) Can J Stat, 6, pp. 239-255
  • Bianco, A., Boente, G., Robust estimators under a semiparametric partly linear autoregression model: asymptotic behavior and bandwidth selection (2007) J Time Ser Anal, 28, pp. 274-306
  • Boente, G., Fraiman, R., Robust nonparametric regression estimation (1989) J Multivar Anal, 29, pp. 180-198
  • Boente, G., Martínez, A., Estimating additive models with missing responses (2016) Commun Stat Theory Methods, 45, pp. 413-426
  • Boente, G., Fraiman, R., Meloche, J., Robust plug-in bandwidth estimators in nonparametric regression (1997) J Stat Plan Inference, 57, pp. 109-142
  • Boente, G., González-Manteiga, W., Pérez-González, A., Robust nonparametric estimation with missing data (2009) J Stat Plan Inference, 139, pp. 571-592
  • Boente, G., Ruiz, M., Zamar, R., On a robust local estimator for the scale function in heteroscedastic nonparametric regression (2010) Stat Probab Lett, 80, pp. 1185-1195
  • Buja, A., Hastie, T., Tibshirani, R., Linear smoothers and additive models (with discussion) (1989) Ann Stat, 17, pp. 453-555
  • Cantoni, E., Ronchetti, E., Resistant selection of the smoothing parameter for smoothing splines (2001) Stat Comput, 11, pp. 141-146
  • Chen, R., Härdle, W., Linton, O., Serverance-Lossin, E., Härdle, W., Schimek, M.G., Nonparametric estimation of additive separable regression models (1996) Statistical theory and computational aspects of smoothing. Proceedings of the COMPSTAT 94 satellite meeting. Springer, pp. 247-265
  • Croux, C., Gijbels, I., Prosdocimi, I., Robust estimation of mean and dispersion functions in extended generalized additive models (2011) Biometrics, 68, pp. 31-44
  • Hastie, T.J., Tibshirani, R.J., (1990) Generalized additive models. Monographs on statistics and applied probability No. 43, , Chapman and Hall, London
  • Hengartner, N., Sperlich, S., Rate optimal estimation with the integration method in the presence of many covariates (2005) J Multivar Anal, 95, pp. 246-272
  • Kong, E., Linton, O., Xia, Y., Uniform Bahadur representation for local polynomial estimates of M -regression and its application to the additive model (2010) Econom Theory, 26, pp. 1529-1564
  • Leung, D., Cross-validation in nonparametric regression with outliers (2005) Ann Stat, 33, pp. 2291-2310
  • Leung, D., Marriott, F., Wu, E., Bandwidth selection in robust smoothing (1993) J Nonparametric Stat, 4, pp. 333-339
  • Li, J., (2012) Zheng Z, ,, Zheng M, Robust estimation of additive models based on marginal integration
  • Linton, O., Nielsen, J., A kernel method of estimating structured nonparametric regression based on marginal integration (1995) Biometrika, 82, pp. 93-101
  • Maronna, R., Martin, R.D., Yohai, V., (2006) Robust statistics: theory and methods, , Wiley, New York
  • Martínez-Miranda, M.D., Raya-Miranda, R., González-Manteiga, W., González-Carmona, A., A bootstrap local bandwidth selector for additive models (2008) J Comput Graph Stat, 17, pp. 38-55
  • Nielsen, J., Linton, O., An optimization interpretation of integration and back-fitting estimators for separable nonparametric models (1998) J R Stat Soc, 60, pp. 217-222
  • Raya-Miranda, R., Martínez-Miranda, M.D., Data-driven local bandwidth selection for additive models with missing data (2011) Appl Math Comput, 217, pp. 10328-10342
  • Severance-Lossin, E., Sperlich, S., Estimation of derivatives for additive separable models (1999) Statistics, 33, pp. 241-265
  • Sperlich, S., Linton, O., Härdle, W., Integration and backfitting methods in additive models-finite sample properties and comparison (1999) TEST, 8, pp. 419-458
  • Stone, C.J., Optimal rates of convergence for nonparametric estimators (1980) Ann Stat, 8, pp. 1348-1360
  • Stone, C.J., Optimal global rates of convergence for nonparametric regression (1982) Ann Stat, 10, pp. 1040-1053
  • Stone, C.J., Additive regression and other nonparametric models (1985) Ann Stat, 13, pp. 689-705
  • Tjøstheim, D., Auestad, B., Nonparametric identification of nonlinear time series: selecting significant lags (1994) J Am Stat Assoc, 89, pp. 1410-1430
  • Wang, F., Scott, D., The L1 method for robust nonparametric regression (1994) J Am Stat Assoc, 89, pp. 65-76
  • Wong, R.K.W., Yao, F., Lee, T.C.M., Robust estimation for generalized additive models (2014) J Comput Graph Stat, 23, pp. 270-289


---------- APA ----------
Boente, G. & Martínez, A. (2017) . Marginal integration M-estimators for additive models. Test, 26(2), 231-260.
---------- CHICAGO ----------
Boente, G., Martínez, A. "Marginal integration M-estimators for additive models" . Test 26, no. 2 (2017) : 231-260.
---------- MLA ----------
Boente, G., Martínez, A. "Marginal integration M-estimators for additive models" . Test, vol. 26, no. 2, 2017, pp. 231-260.
---------- VANCOUVER ----------
Boente, G., Martínez, A. Marginal integration M-estimators for additive models. Test. 2017;26(2):231-260.