Asymptotic normality of conditional density estimation in the single index model for functional time series data
AbstractIn 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 12 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
- 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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- Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
- 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.
- 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.
- 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.
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