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Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection

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  • Ana Bianco
  • Graciela Boente

Abstract

. 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.

Suggested Citation

  • Ana Bianco & Graciela Boente, 2007. "Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 274-306, March.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:2:p:274-306
    DOI: 10.1111/j.1467-9892.2006.00511.x
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    Cited by:

    1. Bianco, Ana & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2010. "Estimation of the marginal location under a partially linear model with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 546-564, February.
    2. Bianco, Ana M. & Spano, Paula M., 2017. "Robust estimation in partially linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 46-64.
    3. Boente, Graciela & Pardo-Fernández, Juan Carlos, 2016. "Robust testing for superiority between two regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 151-168.
    4. Graciela Boente & Alejandra Martínez & Matías Salibián-Barrera, 2017. "Robust estimators for additive models using backfitting," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 744-767, October.
    5. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    6. Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2012. "Bandwidth choice for robust nonparametric scale function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1594-1608.
    7. Graciela Boente & Alejandra Martínez, 2017. "Marginal integration M-estimators for additive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 231-260, June.
    8. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    9. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    10. Zhao, Ge & Ma, Yanyuan, 2016. "Robust nonparametric kernel regression estimator," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 72-79.

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