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A note on the conditional density estimate in the single functional index model

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  • Attaoui, Said
  • Laksaci, Ali
  • Ould Said, Elias

Abstract

In this paper, we consider the estimation of the conditional density of a scalar response variable Y, given a Hilbertian random variable X when the observations are linked with a single-index structure. We establish the pointwise and the uniform almost complete convergence (with the rate) of the kernel estimate of this model. As an application, we show how our result can be applied in the prediction problem via the conditional mode estimate. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is also discussed but not tackled.

Suggested Citation

  • Attaoui, Said & Laksaci, Ali & Ould Said, Elias, 2011. "A note on the conditional density estimate in the single functional index model," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 45-53, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:45-53
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    References listed on IDEAS

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    1. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
    2. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    3. M'hamed Ezzahrioui & Elias Ould Saïd, 2010. "Some asymptotic results of a non‐parametric conditional mode estimator for functional time‐series data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 171-201, May.
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    Cited by:

    1. 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.
    2. Ling, Nengxiang & Xu, Qian, 2012. "Asymptotic normality of conditional density estimation in the single index model for functional time series data," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2235-2243.
    3. Kadiri Nadia & Rabhi Abbes & Bouchentouf Amina Angelika, 2018. "Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship," Dependence Modeling, De Gruyter, vol. 6(1), pages 197-227, November.
    4. 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.
    5. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    6. 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.
    7. Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 257-286, July.
    8. Zhiqiang Jiang & Zhensheng Huang & Jing Zhang, 2023. "Functional single-index composite quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 595-603, July.

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