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Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications

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  • Said Attaoui

    (University of Sciences and Technology, Mohamed Boudiaf)

  • Nengxiang Ling

    (Hefei University of Technology)

Abstract

In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:5:d:10.1007_s00184-015-0564-6
    DOI: 10.1007/s00184-015-0564-6
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Nengxiang Ling & Lilei Cheng & Philippe Vieu & Hui Ding, 2022. "Missing responses at random in functional single index model for time series data," Statistical Papers, Springer, vol. 63(2), pages 665-692, April.
    3. 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.
    4. Akkal Fatima & Kadiri Nadia & Rabhi Abbes, 2021. "Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(1), pages 1-24, March.
    5. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.

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