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Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

Author

Listed:
  • Kadiri Nadia

    (University Djillali Liabes of Sidi Bel Abbes, Algeria)

  • Mekki Sanaà Dounya

    (Department of Mathematics and Computer Science, University Center Salhi Ahmed of Naâama, Algeria)

  • Rabhi Abbes

    (University Djillali Liabes of Sidi Bel Abbes, Algeria)

Abstract

The primary goal of this research was to estimate the quantile of a conditional distribution using a semi-parametric approach in the presence of randomly missing data, where the predictor variable belongs to a semi-metric space. The authors assumed a single index structure to link the explanatory and response variable. First, a kernel estimator was proposed for the conditional distribution function, assuming that the data were selected from a stationary process with missing data at random (MAR). By imposing certain general conditions, the study established the model’s uniform almost complete consistencies with convergence rates.

Suggested Citation

  • Kadiri Nadia & Mekki Sanaà Dounya & Rabhi Abbes, 2023. "Single Functional Index Quantile Regression for Functional Data with Missing Data at Random," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(3), pages 1-19, September.
    • Handle: RePEc:vrs:eaiada:v:27:y:2023:i:3:p:1-19:n:1
    DOI: 10.15611/eada.2023.3.01
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    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    functional data analysis; functional single index process; kernel estimator; missing at random; nonparametric 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
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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