The scalar-on-function modal regression for functional time series data

References

• Aneiros, G., Cao, R., Fraiman, R., Genest, C., and Vieu, P. (2019), ‘Recent Advances in Functional Data Analysis and High-dimensional Statistics’, Journal of Multivariate Analysis, 170, 3–9.
   Web of Science ®Google Scholar
• Azzi, A., Laksaci, A., and Ould-Said, E. (2021), ‘On the Robustification of the Kernel Estimator of the Functional Modal Regression’, Statistics & Probability Letters, 181, 109256.
   Web of Science ®Google Scholar
• Bosq, D. (2000), Linear Processes in Function Spaces: Theory and Applications, Lecture Notes in Statistics, 149, New York: Springer.
   Google Scholar
• Bouanani, O., Rahmani, S., Laksaci, A., and Rachdi, M. (2020), ‘Asymptotic Normality of Conditional Mode Estimation for Functional Dependent Data’, Indian Journal of Pure and Applied Mathematics, 51(2), 465–481.
   Web of Science ®Google Scholar
• Bouzebda, S., Laksaci, A., and Mohammedi, M. (2022), ‘Single Index Regression Model for Functional Quasi-associated Times Series Data’, REVSTAT, 20(5), 605–635.
   Web of Science ®Google Scholar
• Chowdhury, J., and Chaudhuri, P. (2020), ‘Convergence Rates for Kernel Regression in Infinite-dimensional Spaces’, Annals of the Institute of Statistical Mathematics, 72(2), 471–509.
   Web of Science ®Google Scholar
• Cuevas, A. (2014), ‘A Partial Overview of the Theory of Statistics with Functional Data’, Journal of Statistical Planning and Inference, 147, 1–23.
   Web of Science ®Google Scholar
• Dabo-Niang, S., Kaid, Z., and Laksaci, A. (2015), ‘Asymptotic Properties of the Kernel Estimate of Spatial Conditional Mode when the Regressor is Functional’, AStA Advances in Statistical Analysis, 99(2), 131–160.
   Web of Science ®Google Scholar
• Engle, R.F. (1982), ‘Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation’, Econometrica, 50(4), 987–1007.
   Web of Science ®Google Scholar
• Ezzahrioui, M., and Ould-Saïd, E. (2010), ‘Some Asymptotic Results of a Nonparametric Conditional Mode Estimator for Functional Time-series Data’, Statistica Neerlandica, 64(2), 171–201.
   Web of Science ®Google Scholar
• Ferraty, F., Goia, A., and Vieu, P. (2002), ‘Functional Nonparametric Model for Time Series: a Fractal Approach for Dimension Reduction’, Test, 11(2), 317–344.
   Web of Science ®Google Scholar
• Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis, Springer Series in Statistics, New York: Springer.
   Google Scholar
• Goia, A., and Vieu, P. (2016), ‘An Introduction to Recent Advances in High/infinite Dimensional Statistics [Editorial]’, Journal of Multivariate Analysis, 146, 1–6.
   Web of Science ®Google Scholar
• Hörmann, S., Horváth, L., and Reeder, R. (2013), 'A Functional Version of the ARCH Model', Econometric Theory, 29(2), 267–288.
   Web of Science ®Google Scholar
• Jones, D.J. (1978), ‘Nonlinear Autoregressive Processes’, Proceedings of the Royal Society London A, 360, 71–95.
   Google Scholar
• Laib, N., and Louani, D. (2010), ‘Nonparametric Kernel Regression Estimation for Functional Stationary Ergodic Data: Asymptotic Properties’, Journal of Multivariate Analysis, 101(10), 2266–2281.
   Web of Science ®Google Scholar
• Ling, N., and Liu, Y. (2017), ‘The Kernel Regression Estimation for Randomly Censored Functional Stationary Ergodic Data’, Communications in Statistics – Theory and Methods, 46(17), 8557–8574.
   Web of Science ®Google Scholar
• Ling, N., Liu, Y., and Vieu, P. (2016), ‘Conditional Mode Estimation for Functional Stationary Ergodic Data with Responses Missing At Random’, Statistics, 50(5), 991–1013.
   Web of Science ®Google Scholar
• Ling, N., and Vieu, P. (2018), ‘Nonparametric Modelling for Functional Data: Selected Survey and Tracks for Future’, Statistics, 52(4), 934–949.
   Web of Science ®Google Scholar
• Masry, E. (2005), ‘Nonparametric Regression Estimation for Dependent Functional Data: Asymptotic Normality’, Stochastic Processes and Their Applications, 115(1), 155–177.
   Web of Science ®Google Scholar
• Wang, L. (2020), ‘Nearest Neighbors Estimation for Long Memory Functional Data’, Statistical Methods & Applications, 29(4), 709–725.
   Web of Science ®Google Scholar