Robust estimators under semi-parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection
In this article, under a semi-parametric partly linear autoregression model, a family of robust estimators for the autoregression parameter and the autoregression function is studied. The proposed estimators are based on a three-step procedure, in which robust regression estimators and robust smooth...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2007
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 13219caa a22011057a 4500 | ||
|---|---|---|---|
| 001 | PAPER-6695 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203624.0 | ||
| 008 | 190411s2007 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-33847180567 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a JTSAD | ||
| 100 | 1 | |a Bianco, A. | |
| 245 | 1 | 0 | |a Robust estimators under semi-parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection |
| 260 | |c 2007 | ||
| 270 | 1 | 0 | |m Bianco, A.; Instituto de Cálculo, Ciudad Universitaria, Pabellón 2, Buenos Aires, C1428 EHA, Argentina; email: abianco@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a ANDREWS, D., Asymptotics for semiparametric econometric models via stochastic equicontinuity (1994) Econometrica, 62, pp. 43-72 | ||
| 504 | |a ANDREWS, D., POLLARD, D., An introduction to functional central limit theorems for dependent stochastic processes (1994) International Statistical Review, 62, pp. 119-132 | ||
| 504 | |a ANSLEY, C. and WECKER, W. (1983) Extension and examples of the signal extraction approach to regression. In Applied Time Series Analysis of Economic Data (ed. ARNOLD ZELLNER). Economic Research Report ER-5. Washington, DC: U.S. Bureau of the Census, 181-92; ARCONES, M., Weak convergence of stochastic processes indexed by smooth functions (1996) Stochastic Processes and their Application, 62, pp. 11-138 | ||
| 504 | |a BIANCO, A., BOENTE, G., On the asymptotic behaviour of one-step estimates in heteroscedastic regression models (2001) Statistics and Probability Letters, 60, pp. 33-47 | ||
| 504 | |a BIANCO, A., BOENTE, G., A robust approach to partly linear autoregressive models (2002) Estadística, 54, pp. 249-287 | ||
| 504 | |a BIANCO, A., BOENTE, G., Robust estimators in semi-parametric partly linear regression models (2004) Journal of Statistical Planning and Inference, 122, pp. 229-252 | ||
| 504 | |a BIANCO, A., GARCIA BEN, M., MARTINEZ, E. and YOHAI, V. (1996) Robust procedures for regression models with ARIMA errors. In COMPSTAT 96 (ed. ALBERT PRAT). Proceedings in Computational Statistics. Heidelberg: Physica-Verlag, 27-38; BILLINGSLEY, P., (1968) Convergence of Probability Measures, , New York: Wiley | ||
| 504 | |a BOENTE, G., FRAIMAN, R., Robust nonparametric regression estimation (1989) Journal Multivariate Analysis, 29, pp. 180-198 | ||
| 504 | |a BOENTE, G., FRAIMAN, R., Strong uniform convergence rates for some robust equivariant nonparametric regression estimates for mixing processes (1991) International Statistical Review, 59, pp. 355-372 | ||
| 504 | |a BOENTE, G. and FRAIMAN, R. (1991b) A functional approach to robust nonparametric regression. In Directions in Robust Statistics and Diagnostics (eds W. STAHEL and S. WEISBERG). Proceedings of the IMA Institute, USA 33 (Part I), 35-46; BOENTE, G., RODRIGUEZ, D., Robust estimators of high order derivatives of regression functions (2006) Statistics and Probability Letters, 76, pp. 1335-1344 | ||
| 504 | |a 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 | ||
| 504 | |a BOSQ, D., (1996) Nonparametric Statistics for Stochastic Processes. Estimation and Prediction, , New York: Springer-Verlag | ||
| 504 | |a BRILLINGER, D. R. (1986) Discussion of 'Influence functionals for time series' by Martin R. D. and Yohai, V. J. Annals of Statistical 14, 819-22; CAMPBELL, M.J., WALKER, A.M., A survey of statistical work on the Mackenzie river series of annual Canadian lynx trapping on the years 1821-1934 and a new analysis (1977) Journal of the Royal Statistical Society Series A, 140, pp. 411-431 | ||
| 504 | |a CANTONI, E., RONCHETTI, E., Resistant selection of the smoothing parameter for smoothing splines (2001) Statistics and Computing, 11, pp. 141-146 | ||
| 504 | |a CHEN, H., Convergence rates for parametric components in a partly linear model (1988) Annals of Statistics, 16, pp. 136-146 | ||
| 504 | |a CHEN, H., CHEN, K., Selection of the splined variables and convergence rates in a partial spline model (1991) Canadian Journal of Statistics, 19, pp. 323-339 | ||
| 504 | |a CHEN, H., SHIAU, J., A two-stage spline smoothing method for partially linear models (1991) Journal of Statistical Planning and Inference, 25, pp. 187-201 | ||
| 504 | |a CHEN, H., SHIAU, J., Data-driven efficient estimates for partially linear models (1994) Annals of Statistics, 22, pp. 211-237 | ||
| 504 | |a CHU, C.K., MARRON, S., Comparison of two bandwidth selectors with dependent errors (1991) Annals of Statistics, 19, pp. 1906-1918 | ||
| 504 | |a DOUKHAN, P., (1994) Mixing Properties and Examples. Lecture Notes in Statistics, 85. , New York: Springer-Verlag | ||
| 504 | |a DOUKHAN, P., MASSART, P., RIO, E., The central limit theorem for strongly mixing processes (1994) Annales de l' Institut Henri Poincaré (B) Probabilités et Statistiques, 30, pp. 63-82 | ||
| 504 | |a ENGLE, R., GRANGER, C., RICE, J., WEISS, A., semi-parametric estimates of the relation between weather and electricity sales (1986) Journal of the American Statistical Association, 81, pp. 310-320 | ||
| 504 | |a GAO, J., (1992) A Large Sample Theory in semi-parametric Regression Models, , PhD Thesis, University of Science and Technology of China, Hefei, China | ||
| 504 | |a GAO, J., Asymptotic theory for partly linear models (1995) Communications in Statistics, Theory & Methods, 24, pp. 1985-2010 | ||
| 504 | |a GAO, J., Semi-parametric regression smoothing of nonlinear time series (1998) Scandinavian Journal of Statistics, 25, pp. 521-539 | ||
| 504 | |a GAO, J., LIANG, H., Asymptotic normality of pseudo-LS estimator for partly linear autoregression models (1995) Statistics and Probability Letters, 23, pp. 27-34 | ||
| 504 | |a GAO, J., SHI, P., M-type smoothing splines in nonparametric and semi-parametric regression models (1997) Statistica Sinica, 7, pp. 1155-1169 | ||
| 504 | |a GAO, J., YEE, T., Adaptive estimation in partly linear autoregressive models (2000) Canadian Journal of Statistics, 28, pp. 571-586 | ||
| 504 | |a GAO, J., ZHAO, L., Adaptive estimation in partly linear regression models (1993) Science in China, Ser. A, 1, pp. 14-27 | ||
| 504 | |a GREEN, P., JENNISON, C., SEHEULT, A., Analysis of field experiments by least squares smoothing (1985) Journal of the Royal Statistical Society Series B, 47, pp. 299-315 | ||
| 504 | |a GYÖRFI, L., HÄRDLE, W., SARDA, P., VIEU, P., (1989) Nonparametric Curve Estimation from Time Series. Lecture Notes in Statistics, 60. , Berlin: Springer-Verlag | ||
| 504 | |a HÄRDLE, W., (1990) Applied Nonparametric Regression, , Cambridege: Cambridge University Press | ||
| 504 | |a HÄRDLE, W., GASSER, T., On robust kernel estimation of derivatives of regression functions (1985) Scandinanian Journal Statistics, 12, pp. 233-240 | ||
| 504 | |a HÄRDLE, W., LIANG, H., GAO, J., (2000) Partially Linear Models, , Heidelberg: Physica-Verlag | ||
| 504 | |a HART, J., Some automated methods of smoothing time-dependent data (1996) Nonparametric Statistics, 6, pp. 115-142 | ||
| 504 | |a HART, P., VIEU, P., Data-driven bandwidth choice for density estimation based on dependent data (1990) Annals of Statistics, 18, pp. 873-890 | ||
| 504 | |a HE, X., ZHU, Z., FUNG, W., Estimation in a semiparametric model for longitudinal data with unspecified dependence structure (2002) Biometrika, 89, pp. 579-590 | ||
| 504 | |a HECKMAN, N., Spline smoothing in a partly linear model (1986) Journal of the Royal Statistical Society Series B, 48, pp. 244-248 | ||
| 504 | |a IBRAGIMOV, I., LINNIK, Y., (1971) Independent and Stationary Sequences of Random Variables, , Groningen: Wolters-Noerdhoff | ||
| 504 | |a LEUNG, D.H.Y., MARRIOTT, F.H.C., WU, E.K.H., Bandwidth selection in robust smoothing (1993) Journal of Nonparametric Statistics, 2, pp. 333-339 | ||
| 504 | |a LIANG, H., Asymptotically efficient estimators in a partly linear autoregressive model (1996) System Sciences and Mathematical Sciences, 9, pp. 164-170 | ||
| 504 | |a MARTIN, R.D., YOHAI, V.J., Influence functionals for time series (1986) Annals of Statistics, 14, pp. 781-818 | ||
| 504 | |a POLLARD, D., (1984) Convergence of Stochastic Processes, , New York: Springer-Verlag | ||
| 504 | |a RIO, E., Covariance inequalities for strongly mixing processes (1993) Annales de l' Institut Henri Poincaré (B) Probabilités et Statistiques, 29, pp. 587-597 | ||
| 504 | |a ROBINSON, P.M., Nonparametric estimators for time series (1983) Journal of Time Series Analysis, 4, pp. 185-206 | ||
| 504 | |a ROBINSON, P. M. (1984) Robust nonparametric autoregression. In Robust and Nonlinear Time Series Analysis (eds J. FRANKE, W. HÄRDLE and D. MARTIN). Lecture Notes in Statistics, 4. Berlin: Springer-Verlag, 185-206; ROBINSON, P., Root-n-consistent semi-parametric regression (1988) Econometrica, 56, pp. 931-954 | ||
| 504 | |a ROSENBLATT, M., A central limit theorem and a strong mixing condition (1956) Proceedings of the National Academy of Sciences USA, 42, pp. 43-47 | ||
| 504 | |a ROUSSEEUW, P., LEROY, A., (1987) Robust Regression and Outlier Detection, , New York: Wiley | ||
| 504 | |a SEVERINI, T., STANISWALIS, J., Quasi-likelihood estimation in semi-parametric models (1994) Journal of the American Statistical Association, 89, pp. 501-511 | ||
| 504 | |a SEVERINI, T., WONG, W., Profile likelihood and conditionally parametric models (1992) Annals of Statistics, 20, pp. 1768-1802 | ||
| 504 | |a SPECKMAN, P., Kernel smoothing in partial linear models (1988) Journal of the Royal Statistical Society, Series B, 50, pp. 413-436 | ||
| 504 | |a TONG, H., Some comments on the Canadian lynx data (with discussion) (1977) Journal of the Royal Statistical Society Series A, 140, pp. 432-436 | ||
| 504 | |a WANG, F., SCOTT, D., The L1 method for robust nonparametric regression (1994) Journal of the American Statistical Association, 89, pp. 65-76 | ||
| 504 | |a WONG, C.M., KOHN, R., A Bayesian approach to estimating and forecasting additive nonparametric autoregressive models (1996) Journal of Time Series Analysis, 17, pp. 203-220 | ||
| 504 | |a YAO, Q., TONG, H., On the subset selection in nonparametric stochastic regression (1994) Statistica Sinica, 4, pp. 51-70 | ||
| 504 | |a YEE, T., WILD, C., Vector generalized additive models (1996) Journal of the Royal Statistical Society Series B, 58, pp. 481-493 | ||
| 504 | |a YOHAI, V., High breakdown point and high efficiency robust estimates for regression (1987) Annals of Statistics, 15, pp. 642-656 | ||
| 504 | |a YOHAI, V., ZAMAR, R., High breakdown estimates of regression by means of the minimization of an efficient scale (1988) Journal of American Statistical Association, 83, pp. 406-413 | ||
| 504 | |a YU, B., Rates of convergence of empirical processes for stationary mixing sequences (1994) Annals of Probability, 22, pp. 94-116 | ||
| 520 | 3 | |a In this article, under a semi-parametric partly linear autoregression model, a family of robust estimators for the autoregression parameter and the autoregression function is studied. The proposed estimators are based on a three-step procedure, in which robust regression estimators and robust smoothing techniques are combined. Asymptotic results on the autoregression estimators are derived. Besides combining robust procedures with M-smoothers, predicted values for the series and detection residuals, which allow to detect anomalous data, are introduced. Robust cross-validation methods to select the smoothing parameter are presented as an alternative to the classical ones, which are sensitive to outlying observations. A Monte Carlo study is conducted to compare the performance of the proposed criteria. Finally, the asymptotic distribution of the autoregression parameter estimator is stated uniformly over the smoothing parameter. © 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd. |l eng | |
| 593 | |a Instituto de Cálculo, Ciudad Universitaria, Pabellón 2, Buenos Aires, C1428 EHA, Argentina | ||
| 690 | 1 | 0 | |a ASYMPTOTIC PROPERTIES |
| 690 | 1 | 0 | |a CROSS-VALIDATION |
| 690 | 1 | 0 | |a FILTERING |
| 690 | 1 | 0 | |a PARTLY LINEAR AUTOREGRESSION |
| 690 | 1 | 0 | |a PREDICTION |
| 690 | 1 | 0 | |a RATE OF CONVERGENCE |
| 690 | 1 | 0 | |a ROBUST ESTIMATION |
| 690 | 1 | 0 | |a SMOOTHING TECHNIQUES |
| 700 | 1 | |a Boente, G. | |
| 773 | 0 | |d 2007 |g v. 28 |h pp. 274-306 |k n. 2 |p J. Time Ser. Anal. |x 01439782 |w (AR-BaUEN)CENRE-252 |t Journal of Time Series Analysis | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-33847180567&doi=10.1111%2fj.1467-9892.2006.00511.x&partnerID=40&md5=94a7ba38f999197dc7e950c025c1c40e |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1111/j.1467-9892.2006.00511.x |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_01439782_v28_n2_p274_Bianco |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01439782_v28_n2_p274_Bianco |y Registro en la Biblioteca Digital |
| 961 | |a paper_01439782_v28_n2_p274_Bianco |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 67648 | ||