Artículo

Agostinelli, C.; Bianco, A.M.; Boente, G."Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter" (2019) Annals of the Institute of Statistical Mathematics
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:

This paper develops a robust profile estimation method for the parametric and nonparametric components of a single-index model when the errors have a strongly unimodal density with unknown nuisance parameter. We derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single-index parameter estimators. Under a log-Gamma model, the sensitivity to anomalous observations is studied using the empirical influence curve. We also discuss a robust K-fold cross-validation procedure to select the smoothing parameters. A numerical study carried on with errors following a log-Gamma model and for contaminated schemes shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one. A real data set illustrates the use of our proposal. © 2019, The Institute of Statistical Mathematics, Tokyo.

Registro:

Documento: Artículo
Título:Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter
Autor:Agostinelli, C.; Bianco, A.M.; Boente, G.
Filiación:Dipartimento di Matematica, Università di Trento, Via Sommarive, 14, Trento, 38123, Italy
Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires, 1428, Argentina
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:Fisher consistency; Kernel weights; Local polynomials; Robustness; Single-index models; Errors; Robustness (control systems); Asymptotic distributions; Fisher consistency; K fold cross validations; Kernel weight; Local polynomials; Robustness properties; Single index models; Smoothing parameter; Parameter estimation
Año:2019
DOI: http://dx.doi.org/10.1007/s10463-019-00712-8
Handle:http://hdl.handle.net/20.500.12110/paper_00203157_v_n_p_Agostinelli
Título revista:Annals of the Institute of Statistical Mathematics
Título revista abreviado:Annal. Inst. Stat. Math.
ISSN:00203157
CODEN:AISXA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00203157_v_n_p_Agostinelli

Referencias:

  • Aït Sahalia, Y., (1995) The Delta Method for Nonaparmetric Kernel Functionals, , Ph.D. dissertation, University of Chicago
  • Bianco, A., Boente, G., On the asymptotic behavior of one-step estimation (2002) Statistics and Probability Letters, 60, pp. 33-47
  • Bianco, A., Boente, G., Robust estimators under a semiparametric partly linear autoregression model: asymptotic behavior and bandwidth selection (2007) Journal of Time Series Analysis, 28, pp. 274-306
  • Bianco, A., García Ben, M., Yohai, V., Robust estimation for linear regression with asymmetric errors (2005) Canadian Journal Statistics, 33, pp. 511-528
  • Boente, G., Fraiman, R., Meloche, J., Robust plug-in bandwidth estimators in nonparametric regression (1997) Journal of Statistical Planning and Inference, 57, pp. 109-142
  • Boente, G., Rodriguez, D., Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis (2008) Computational Statistics and Data Analysis, 52, pp. 2808-2828
  • Boente, G., Rodriguez, D., Robust inference in generalized partially linear models (2010) Computational Statistics and Data Analysis, 54, pp. 2942-2966
  • Boente, G., Rodriguez, D., Robust estimates in generalized partially linear single-index models (2012) TEST, 21, pp. 386-411
  • Cantoni, E., Ronchetti, E., Resistant selection of the smoothing parameter for smoothing splines (2001) Statistics and Computing, 11, pp. 141-146
  • Cantoni, E., Ronchetti, E., A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures (2006) Journal of Health Economics, 25, pp. 198-213
  • Carroll, R., Fan, J., Gijbels, I., Wand, M., Generalized partially linear single-index models (1997) Journal of the American Statistical Association, 92, pp. 477-489
  • Chang, Z.Q., Xue, L.G., Zhu, L.X., On an asymptotically more efficient estimation of the single-index model (2010) Journal of Multivariate Analysis, 101, pp. 1898-1901
  • Croux, C., Ruiz-Gazen, A., High breakdown estimators for principal components: the projection-pursuit approach revisited (2005) Journal of Multivariate Analysis, 95, pp. 206-226
  • Delecroix, M., Hristache, M., Patilea, V., On semiparametric M -estimation in single-index regression (2006) Journal of Statistical Planning and Inference, 136, pp. 730-769
  • Hampel, F.R., The influence curve and its role in robust estimation (1974) Journal of the American Statistical Association, 69, pp. 383-394
  • Härdle, W., Hall, P., Ichimura, H., Optimal smoothing in single-index models (1993) Annals of Statistics, 21, pp. 157-178
  • Härdle, W., Stoker, T.M., Investigating smooth multiple regression by method of average derivatives (1989) Journal of the American Statistical Association, 84, pp. 986-995
  • Hubert, M., Vandervieren, E., An adjusted boxplot for skewed distributions (2008) Computational Statistics and Data Analysis, 52, pp. 5186-5201
  • Leung, D., Cross-validation in nonparametric regression with outliers (2005) Annals of Statistics, 33, pp. 2291-2310
  • Leung, D., Marriott, F., Wu, E., Bandwidth selection in robust smoothing (1993) Journal of Nonparametric Statistics, 4, pp. 333-339
  • Li, W., Patilea, W., A new inference approach for single-index models (2017) Journal of Multivariate Analysis, 158, pp. 47-59
  • Liu, J., Zhang, R., Zhao, W., Lv, Y., A robust and efficient estimation method for single index models (2013) Journal of Multivariate Analysis, 122, pp. 226-238
  • Mallows, C., (1974) On Some Topics in Robustness, , Memorandum, Bell Laboratories, Murray Hill, N.J
  • Manchester, L., Empirical influence for robust smoothing (1996) Australian Journal of Statistics, 38, pp. 275-296
  • Marazzi, A., Yohai, V., Adaptively truncated maximum likelihood regression with asymmetric errors (2004) Journal of Statistical Planning and Inference, 122, pp. 271-291
  • Maronna, R., Martin, D., Yohai, V., (2006) Robust statistics: Theory and methods, , Wiley, New York
  • Pollard, D., (1984) Convergence of stochastic processes. Springer series in statistics, , Springer, New York
  • Powell, J.L., Stock, J.H., Stoker, T.M., Semiparametric estimation of index coefficients (1989) Econometrica, 57, pp. 1403-1430
  • Rodriguez, D., (2007) Estimación robusta en modelos parcialmente lineales generalizados, , http://cms.dm.uba.ar/academico/carreras/doctorado/tesisdanielarodriguez.pdf, Ph.D. Thesis (in spanish), Universidad de Buenos Aires, Accessed 20 Feb 2019
  • Rousseeuw, P.J., Yohai, V.J., Robust regression by means of S -estimators (1984) Robust and Nonlinear Time Series, Lecture Notes in Statistics, 26, pp. 256-272. , J. Franke, W. Hardle, D. Martin, New York, Springer
  • Severini, T., Staniswalis, J., Quasi-likelihood estimation in semiparametric models (1994) Journal of the American Statistical Association, 89, pp. 501-511
  • Severini, T., Wong, W., Profile likelihood and conditionally parametric models (1992) Annals of Statistics, 20 (4), pp. 1768-1802
  • Sherman, R., Maximal inequalities for degenerate U -processes with applications to optimization estimators (1994) Annals of Statistics, 22, pp. 439-459
  • Sun, Y., Genton, M.G., Functional boxplots (2011) Journal of Computational and Graphical Statistics, 20, pp. 316-334
  • Tamine, J., (2002) Smoothed influence function: Another view at robust nonparametric regression, , Discussion paper 62, Sonderforschungsbereich 373, Humboldt-Universiät zu Berlin
  • Tukey, J., (1977) Exploratory data analysis, , Addison-Wesley, Reading, MA
  • van der Vaart, A., Estimating a real parameter in a class of semiparametric models (1988) Annals of Statistics, 16 (4), pp. 1450-1474
  • Wang, F., Scott, D., The L1 method for robust nonparametric regression (1994) Journal of the American Statistical Association, 89, pp. 65-76
  • Wang, Q., Zhang, T., Hädle, W., (2014) An Extended Single Index Model with Missing Response at Random, , SFB 649 Discussion Paper 2014-003
  • Wu, T.Z., Yu, K., Yu, Y., Single index quantile regression (2010) Journal of Multivariate Analysis, 101, pp. 1607-1621
  • Xia, Y., Härdle, W., Semi-parametric estimation of partially linear single-index models (2006) Journal of Multivariate Analysis, 97, pp. 1162-1184
  • Xia, Y., Härdle, W., Linton, O., Optimal smoothing for a computationally and efficient single index estimator (2012) Exploring Research Frontiers in Contemporary Statistics and Econometrics: A Festschrift for Léopold Simar, pp. 229-261
  • Xia, Y., Tong, H., Li, W.K., Zhu, L., An adaptive estimation of dimension reduction space (with discussion) (2002) Journal of the Royal Statistical Society, Series B, 64, pp. 363-410
  • Xue, L.G., Zhu, L.X., Empirical likelihood for single-index model (2006) Journal of Multivariate Analysis, 97, pp. 1295-1312
  • Zhang, R., Huang, R., Lv, Z., Statistical inference for the index parameter in single-index models (2010) Journal of Multivariate Analysis, 101, pp. 1026-1041

Citas:

---------- APA ----------
Agostinelli, C., Bianco, A.M. & Boente, G. (2019) . Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter. Annals of the Institute of Statistical Mathematics.
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- CHICAGO ----------
Agostinelli, C., Bianco, A.M., Boente, G. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter" . Annals of the Institute of Statistical Mathematics (2019).
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- MLA ----------
Agostinelli, C., Bianco, A.M., Boente, G. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter" . Annals of the Institute of Statistical Mathematics, 2019.
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- VANCOUVER ----------
Agostinelli, C., Bianco, A.M., Boente, G. Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter. Annal. Inst. Stat. Math. 2019.
http://dx.doi.org/10.1007/s10463-019-00712-8