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Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring

Author

Listed:
  • Hamri Mohamed Mehdi

    (LABRI, ESI, Sidi Bel Abbes, University Djillali Liabes of Sidi Bel Abbes, Sidi Bel Abbes, Algeria)

  • Mekki Sanaà Dounya

    (Department of Mathematics and Computer Science, University Center Salhi Ahmed of Naâma, Sidi Bel Abbes, Algeria)

  • Rabhi Abbes

    (University Djillali Liabes of Sidi Bel Abbes, Sidi Bel Abbes, Algeria)

  • Kadiri Nadia

    (University Djillali Liabes of Sidi Bel Abbes, Sidi Bel Abbes, Algeria)

Abstract

The main objective of this paper was to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Then the paper gives an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Finally, a simulation study was carried out to evaluate the performance of this estimate.

Suggested Citation

  • Hamri Mohamed Mehdi & Mekki Sanaà Dounya & Rabhi Abbes & Kadiri Nadia, 2022. "Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(1), pages 31-62, March.
    • Handle: RePEc:vrs:eaiada:v:26:y:2022:i:1:p:31-62:n:1
    DOI: 10.15611/eada.2022.1.03
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    References listed on IDEAS

    as
    1. Einmahl, J.H.J. & Deheuvels, P., 2000. "Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications," Other publications TiSEM ac9bbdc0-62f8-4b48-9a84-1, Tilburg University, School of Economics and Management.
    2. Lemdani, Mohamed & Ould-Saïd, Elias & Poulin, Nicolas, 2009. "Asymptotic properties of a conditional quantile estimator with randomly truncated data," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 546-559, March.
    3. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    4. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    5. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    6. Han-Ying Liang & Jacobo Uña-Álvarez, 2010. "Asymptotic normality for estimator of conditional mode under left-truncated and dependent observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 1-19, July.
    7. Salah Khardani & Mohamed Lemdani & Elias Ould Saïd, 2012. "On the strong uniform consistency of the mode estimator for censored time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 229-241, February.
    8. Mohamed Chaouch & Amina Angelika Bouchentouf & Aboubacar Traore & Abbes Rabhi, 2020. "Single functional index quantile regression under general dependence structure," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 725-755, July.
    9. Said Attaoui & Nengxiang Ling, 2016. "Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 485-511, July.
    10. Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
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    More about this item

    Keywords

    censored data; functional data; kernel estimator; normality; non-parametric estimation; small ball probability;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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