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Asymptotic normality of conditional density estimation in the single index model for functional time series data


  • Ling, Nengxiang
  • Xu, Qian


In this paper, we investigate the estimation of conditional density function based on the single-index model for functional time series data. The asymptotic normality of the conditional density estimator and the conditional mode estimator for the α mixing dependence functional time series data are obtained, respectively. Furthermore, as applications, the asymptotic (1-ζ) confidence interval of the conditional density function and the conditional mode are also presented for 0<ζ<1.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2235-2243 DOI: 10.1016/j.spl.2012.08.018

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    References listed on IDEAS

    1. Laksaci, Ali & Lemdani, Mohamed & Ould-Sad, Elias, 2009. "A generalized L1-approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1065-1073, April.
    2. 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.
    3. Frédéric Ferraty & Ingrid Van Keilegom & Philippe Vieu, 2010. "On the Validity of the Bootstrap in Non-Parametric Functional Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 286-306.
    4. 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.
    5. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    6. 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.
    7. Azzedine, Nadjia & Laksaci, Ali & Ould-Saïd, Elias, 2008. "On robust nonparametric regression estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3216-3221, December.
    8. 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.
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