IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v154y2017icp59-84.html
   My bibliography  Save this article

Robust estimators in semi-functional partial linear regression models

Author

Listed:
  • Boente, Graciela
  • Vahnovan, Alejandra

Abstract

Partial linear models have been adapted to deal with functional covariates to capture both the advantages of a semi-linear modelling and those of nonparametric modelling for functional data. It is easy to see that the estimation procedures for these models are highly sensitive to the presence of even a small proportion of outliers in the data. To solve the problem of atypical observations when the covariates of the nonparametric component are functional, robust estimates for the regression parameter and regression operator are introduced. Consistency results of the robust estimators and the asymptotic distribution of the regression parameter estimator are studied. The reported numerical experiments show that the resulting estimators have good robustness properties. The benefits of considering robust estimators is also illustrated on a real data set where the robust fit reveals the presence of influential outliers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:59-84
    DOI: 10.1016/j.jmva.2016.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16301178
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    2. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    3. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. Boente, Graciela & Vahnovan, Alejandra, 2015. "Strong convergence of robust equivariant nonparametric functional regression estimators," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 1-11.
    6. 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.
    7. 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.
    8. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
    9. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    10. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    11. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    12. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    13. 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.
    14. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    15. Germán Aneiros-Pérez & Philippe Vieu, 2011. "Automatic estimation procedure in partial linear model with functional data," Statistical Papers, Springer, vol. 52(4), pages 751-771, November.
    16. Azzedine, Nadjia & Laksaci, Ali & Ould-Saïd, Elias, 2008. "On robust nonparametric regression estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3216-3221, December.
    17. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    18. Germán Aneiros-Pérez & Philippe Vieu, 2013. "Testing linearity in semi-parametric functional data analysis," Computational Statistics, Springer, vol. 28(2), pages 413-434, April.
    19. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    20. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
    21. Ana Bianco & Graciela Boente & Elena Martínez, 2006. "Robust Tests in Semiparametric Partly Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 435-450, September.
    22. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    23. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    24. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    25. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    26. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. F. Jamaluddin* & H. H. Ali & S. S. Syed Yahaya & Z. Zain, 2018. "The Performance of Robust Multivariate Ewma Control Charts," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 52-58:6.
    2. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    3. Boente, Graciela & Salibian-Barrera, Matías & Vena, Pablo, 2020. "Robust estimation for semi-functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    4. Martínez-Hernández, Israel & Genton, Marc G. & González-Farías, Graciela, 2019. "Robust depth-based estimation of the functional autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 66-79.
    5. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    2. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.
    3. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    5. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    6. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    7. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.
    8. Shuyu Meng & Zhensheng Huang, 2024. "Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    9. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    10. Bianco, Ana M. & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2015. "Robust inference in partially linear models with missing responses," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 88-98.
    11. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    12. Benhenni, Karim & Hassan, Ali Hajj & Su, Yingcai, 2019. "Local polynomial estimation of regression operators from functional data with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 80-94.
    13. 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.
    14. Ping Yu & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Robust exponential squared loss-based estimation in semi-functional linear regression models," Computational Statistics, Springer, vol. 34(2), pages 503-525, June.
    15. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    16. Wang, Qihua & Härdle, Wolfgang & Linton, Oliver, 2002. "Semiparametric regression analysis under imputation for missing response data," SFB 373 Discussion Papers 2002,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    17. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    18. 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.
    19. Ana M. Bianco & Graciela Boente & Wenceslao González-Manteiga & Ana Pérez-González, 2019. "Plug-in marginal estimation under a general regression model with missing responses and covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 106-146, March.
    20. Haotian Chen & Xibin Zhang, 2014. "Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption," Monash Econometrics and Business Statistics Working Papers 28/14, Monash University, Department of Econometrics and Business Statistics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:59-84. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.