A recursive kernel estimate of the functional modal regression under ergodic dependence condition

References

• Amiri, A., C. Crambes, and B. Thiam. 2014. Recursive estimation of nonparametric regression with functional covariate. Computational Statististics & Data Analysis 69:154–172.
   Web of Science ®Google Scholar
• Attouch, M. K., and W. Bouabça. 2013. The k-nearest neighbors estimation of the conditional mode for functional data. Revue Roumaine Mathemotiques Pures Applqueis 58:393–415.
   Google Scholar
• Bosq, D. 2000. Linear Processes in Function Spaces: Theory and Applications. Vol. 149 of Lecture notes in statistics. New York, NY: Springer-Verlag.
   Google Scholar
• Besse, P., and H. Cardot. 1996. Approximation spline de la prévision d’un processus fonctionnel autorégressif d’ordre 1. Canadian journal of Statistics 24:467–87.
   Web of Science ®Google Scholar
• Collomb, G., W. Härdle, and S. Hassani. 1987. A note on prediction via conditional mode estimation. Journal of Statistical, Planning, and Inference 15:227–36.
   Web of Science ®Google Scholar
• Dabo-Niang, S., and A. Laksaci. 2007. Estimation non paramétrique du mode conditionnel pour variable explicative fonctionnelle. Compte. Rendu Mathematique, Academie des Sciences, Paris 344:49–52.
   Web of Science ®Google Scholar
• Dabo-Niang, S., and A. Laksaci. 2012. On spatial conditional mode estimation for a functional regressor. Statistics & Probability Letters 82:1413–1421.
   Web of Science ®Google Scholar
• Ezzahrioui, M., and E. Ould-Said. 2008. Asymptotic normality of nonparametric estimators of the conditional mode function for functional data. Journal of Nonparametric Statistics 20:3–18.
   Web of Science ®Google Scholar
• Ezzahrioui, M., and E. Ould-Said. 2010. Some asymptotic results of a non-parametric conditional mode estimator for functional time-series data. Statistica Neerlandica 64:171–201.
   Web of Science ®Google Scholar
• Ferraty, F., and P. Vieu. 2006. Nonparametric Functional Data Analysis. Springer Series in Statistics. New York, NY: Springer.
   Google Scholar
• Ferraty, F., A. Laksaci, and P. Vieu. 2006. Estimating some chacteristics of the conditional distribution in nonparametric functional models. Statistical Inference for Stochastic Processes 9:47–76.
   Google Scholar
• Ferraty F., P. Laksaci, A. Tadj, and P. Vieu. 2010. Rate of uniform consistency for nonparametric estimates with functional variables. Journal of Statistical, Planning, and Inference 140:335–352.
   Web of Science ®Google Scholar
• Ferraty, F., A. Mas, and P. Vieu. 2007. Nonparametric regression on functional data: inference and practical aspects. Australian & New Zealand Journal of Statistics 49:267–286
   Web of Science ®Google Scholar
• Gaenssler, P., J. Strobel, and W. Stute. 1978. On central limit theorems for martingale triangular arrays. Acta Mathematica Academiae Scientiarum Hungarica 31:205–216.
   Web of Science ®Google Scholar
• Gheriballah, A., A. Laksaci, and S. Sekkal. 2013. Nonparametric M-regression for functional ergodic data. Statistics Probability Letters 83:902–908.
   Web of Science ®Google Scholar
• Laїb, N., and D. Louani. 2011. Strong consistency of the regression function estimator for functional stationary ergodic data. Journal of Statistical, Planning, and Inference 141:359–372.
   Web of Science ®Google Scholar
• Ling, N., and Q. Xu. 2012. Asymptotic normality of conditional density estimation in the single index model for functional time series data. Statistics & Probability Letters 82:2235–2243.
   Web of Science ®Google Scholar
• Louani, D., and E. Ould-Saïd. 1999. Asymptotic normality of kernel estimators of the conditional mode under strong mixing hypothesis. Journal of Nonparametric Statistics 11:413–442.
   Web of Science ®Google Scholar
• Quintela del Rio, A., and P. Vieu. 1997. A nonparametric conditionnal mode estimate. Journal of Nonparametric Statistics 8:253–266.
   Google Scholar
• Ramsay, J. O., and B. W. Silverman. 2005. Functional Data Analysis, 2nd ed. New York, NY: Springer.
   Google Scholar
• Roussas, G. R., and L. T. Tran. 1989. Asymptotic normality of the recursive kernel regression estimate under dependence conditions. Annals of Statistics 20:98–120.
   Web of Science ®Google Scholar
• Thiam, B. 2006. Recursive estimation of functional. PhD thesis, Universitey Versailles, Versailles, France.
   Google Scholar