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Randomly censored quantile regression estimation using functional stationary ergodic data

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  • Mohamed Chaouch
  • Salah Khardani

Abstract

This paper investigates the conditional quantile estimation of a randomly censored scalar response variable given a functional random covariate (i.e. valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. A kernel-type estimator of the conditional quantile function is introduced. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under mild assumptions. A simulation study is considered to show the performance of the proposed estimator. An application to the electricity peak demand prediction using censored smart meter data is also provided.

Suggested Citation

  • Mohamed Chaouch & Salah Khardani, 2015. "Randomly censored quantile regression estimation using functional stationary ergodic data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 65-87, March.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:65-87
    DOI: 10.1080/10485252.2014.982651
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    5. Goia, Aldo & May, Caterina & Fusai, Gianluca, 2010. "Functional clustering and linear regression for peak load forecasting," International Journal of Forecasting, Elsevier, vol. 26(4), pages 700-711, October.
    6. Ali Gannoun & Jérôme Saracco & Ao Yuan & George E. Bonney, 2005. "Non‐parametric Quantile Regression with Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 527-550, December.
    7. Laib, Naâmane & Louani, Djamal, 2010. "Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2266-2281, November.
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    Cited by:

    1. Salah, Khardani & Yousri, Slaoui, 2019. "Nonparametric relative regression under random censorship model," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 116-122.
    2. Mohamed Chaouch, 2023. "Probabilistic Wind Speed Forecasting for Wind Turbine Allocation in the Power Grid," Energies, MDPI, vol. 16(22), pages 1-15, November.
    3. 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.
    4. 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).
    5. Kamal Boukhetala & Jean-François Dupuy, 2019. "Modélisation Stochastique et Statistique Book of Proceedings," Post-Print hal-02593238, HAL.
    6. Omar Fetitah & Mohammed Kadi Attouch & Salah Khardani & Ali Righi, 2023. "Robust nonparametric equivariant regression for functional data with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 899-929, November.
    7. Haben, Stephen & Arora, Siddharth & Giasemidis, Georgios & Voss, Marcus & Vukadinović Greetham, Danica, 2021. "Review of low voltage load forecasting: Methods, applications, and recommendations," Applied Energy, Elsevier, vol. 304(C).

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