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Classification with incomplete functional covariates

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  • Mojirsheibani, Majid
  • Shaw, Crystal

Abstract

We consider the problem of functional classification when the covariate may be unavailable (unobservable) on some subsets of its domain. Given the observed fragments of the functional covariates, we propose a strongly consistent nonparametric classifier based on local averaging.

Suggested Citation

  • Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:40-46
    DOI: 10.1016/j.spl.2018.03.010
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    References listed on IDEAS

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    1. Bugni, Federico A., 2012. "Specification Test For Missing Functional Data," Econometric Theory, Cambridge University Press, vol. 28(5), pages 959-1002, October.
    2. Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    3. Bravo, Francesco, 2015. "Semiparametric estimation with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 329-346.
    4. Aurore Delaigle & Peter Hall, 2013. "Classification Using Censored Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1269-1283, December.
    5. repec:pri:cheawb:case_paxson_economic_status_paper is not listed on IDEAS
    6. Anne Case & Darren Lubotsky & Christina Paxson, 2002. "Economic Status and Health in Childhood: The Origins of the Gradient," American Economic Review, American Economic Association, vol. 92(5), pages 1308-1334, December.
    7. Timothy Reese & Majid Mojirsheibani, 2017. "On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 81-112, March.
    8. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    9. C. Abraham & G. Biau & B. Cadre, 2006. "On the Kernel Rule for Function Classification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 619-633, September.
    10. Chung Chang & Yakuan Chen & R. Ogden, 2014. "Functional data classification: a wavelet approach," Computational Statistics, Springer, vol. 29(6), pages 1497-1513, December.
    11. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    12. repec:pri:cheawb:case_paxson_economic_status_paper.pdf is not listed on IDEAS
    13. A. Delaigle & P. Hall & N. Bathia, 2012. "Componentwise classification and clustering of functional data," Biometrika, Biometrika Trust, vol. 99(2), pages 299-313.
    14. David Kraus, 2015. "Components and completion of partially observed functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 777-801, September.
    15. Majid Mojirsheibani & Zahra Montazeri, 2007. "Statistical classification with missing covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 839-857, November.
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    Cited by:

    1. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    2. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).

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