Uniform consistency rate of kNN regression estimation for functional time series data

References

• Aneiros, G., Bongiorno, E., Cao, R., and Vieu, P. (2017), ‘An Introduction to the 4th Edition of the International Workshop on Functional and Operatorial Statistics’, in Functional Statistics and Related Fields, Contributions to Statistics, Springer, pp. 1–5.
   Google Scholar
• Aneiros, G., Cao, R., Fraiman, R., Genest, C., and Vieu, P. (2019a), ‘Recent Advances in Functional Data Analysis and High-Dimensional Statistics’, Journal of Multivariate Analysis, 170, forthcoming.
   Web of Science ®Google Scholar
• Aneiros, G., Novo, S., and Vieu, P. (2019b), ‘Automatic and Location-Adaptive Estimation in Functional Single-Index Regression’, Journal of Nonparametric Statistics, in revision.
   Web of Science ®Google Scholar
• Attouch, M.K., and Benchikh, T. (2012), ‘Asymptotic Distribution of Robust K-Nearest Neighbour Estimator for Functional Nonparametric Models’, Matematicki Vesnik, 64(4), 275–285.
   Google Scholar
• Baíllo, A., and Grané, A. (2009), ‘Local Linear Regression for Functional Predictor and Scalar Response’, Journal of Multivariate Analysis, 100(1), 102–111. doi: 10.1016/j.jmva.2008.03.008
   Web of Science ®Google Scholar
• Barrientos-Marin, J., Ferraty, F., and INITSP. Vieu (2010), ‘Locally Modelled Regression and Functional Data’, Journal of Nonparametric Statistics, 22(5), 617–632. doi: 10.1080/10485250903089930
   Web of Science ®Google Scholar
• Biau, G., Cérou, G., and INITSA. Guyader (2010), ‘Rate of Convergence of the Functional k-Nearest Neighbor Estimate’, IEEE Transactions on Information Theory, 56(4), 2034–2040. doi: 10.1109/TIT.2010.2040857
   Web of Science ®Google Scholar
• Bollerslev, T. (1986), ‘Generalized Autoregressive Conditional Heteroskedasticity with Applications in Finance’, General Information, 31(3), 307–327.
   Google Scholar
• Bosq, D. (2000), ‘Linear Processes in Function Spaces. Estimation and prediction’, Lecture Notes in Statistics, 149, Springer, Berlin.
   Google Scholar
• Burba, F., Ferraty, F., and Vieu, P. (2009), ‘k-Nearest Neighbour Method in Functional Nonparametric Regression’, Journal of Nonparametric Statistics, 21(4), 453–469. doi: 10.1080/10485250802668909
   Web of Science ®Google Scholar
• Cuevas, A. (2014), ‘A Partial Overview of the Theory of Statistics with Functional Data’, Jounal of Statistical Planning and Inference, 147, 1–23. doi: 10.1016/j.jspi.2013.04.002
   Web of Science ®Google Scholar
• Delsol, L. (2009), ‘Advances on Asymptotic Normality in Nonparametric Functional Time Series Analysis’, Statistics, 43(1), 13–33. doi: 10.1080/02331880802184961
   Web of Science ®Google Scholar
• Doukhan, P. (1994), ‘Mixing: Properties and Examples’, Lecture Notes in Statistics, 85, Springer-Verlag.
   Google Scholar
• Engle, R.F. (1982), ‘Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation’, Econometrica, 50(4), 987–1007. doi: 10.2307/1912773
   Web of Science ®Google Scholar
• Ezzahrioui, M., and Ould-Saïd, E. (2008), ‘Asymptotic Normality of a Nonparametric Estimator of the Conditional Mode Function for Functional Data’, Journal of Nonparametric Statistics, 20(1), 3–18. doi: 10.1080/10485250701541454
   Web of Science ®Google Scholar
• Ezzahrioui, M., and Ould-Saïd, E. (2010), ‘Some Asymptotic Results of a Non-Parametric Conditional Mode Estimator for Functional Time-Series Data’, Statistica Neerlandica, 64(2), 171–201. doi: 10.1111/j.1467-9574.2010.00449.x
   Web of Science ®Google Scholar
• Ferraty, F., Laksaci, A., Tadj, A., and Vieu, P. (2010), ‘Rate of Uniform Consistency for Nonparametric Estimates with Functional Variables’, Jounal of Statistical Planning and Inference, 140, 335–352. doi: 10.1016/j.jspi.2009.07.019
   Web of Science ®Google Scholar
• Ferraty, F., Mas, A., and Vieu, P. (2007), ‘Nonparametric Regression on Functional Data: Inference and Practical Aspects’, Australian and New Zealand Journal of Statistics, 49(3), 267–286. doi: 10.1111/j.1467-842X.2007.00480.x
   Web of Science ®Google Scholar
• Ferraty, F., Rabhi, A., and Vieu, P. (2005), ‘Conditional Quantiles for Dependent Functional Data with Application to the Climatic El Niño Phenomenon’, Sankhya, 67(2), 378–398.
   Google Scholar
• Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis. Theory and Practice, Berlin: Springer.
   Google Scholar
• Geenens, G. (2011), ‘Curse of Dimensionality and Related Issues in Nonparametric Functional Regression’, Statistics Surveys, 5, 30–43. doi: 10.1214/09-SS049
   Google Scholar
• Goia, A., and Vieu, P. (2016), ‘An Introduction to Recent Advances in High/Infinite Dimensional Statistics’, Journal of Multivariate Analysis, 146, 1–6. doi: 10.1016/j.jmva.2015.12.001
   Web of Science ®Google Scholar
• Greven, S., and Scheipl, F. (2017), ‘A General Framework for Functional Regression Modelling’, Statistical Modelling, 17(1–2), 1–35. doi: 10.1177/1471082X16681317
   Web of Science ®Google Scholar
• Härdle, W., and Vieu, P. (1992), ‘Kernel Regression Smoothing of Time Series’, Journal of Time Series Analysis, 13(3), 209–232. doi: 10.1111/j.1467-9892.1992.tb00103.x
   Google Scholar
• Horváth, L., and Kokoszka, P. (2012), ‘Inference for Functional Data with Applications’, Springer Series in Statistics. Springer, New-York.
   Google Scholar
• Hsing, T., and Eubank, R. (2015), ‘Theoretical Foundations to Functional Data Analysis with an Introduction to Linear Operators’, Wiley Series in Probability and Statistics, Chichester/ John Wiley & Sons.
   Google Scholar
• Kara-Zaitri, L., Laksaci, A., Rachdi, M., and Vieu, P. (2017), ‘Data-Driven kNN Estimation in Nonparametric Functional Data Analysis’, Journal of Multivariate Analysis, 153, 176–188. doi: 10.1016/j.jmva.2016.09.016
   Web of Science ®Google Scholar
• Kudraszow, N.L., and Vieu, P. (2013), ‘Uniform Consistency of kNN Regressors for Functional Variables’, Statistics and Probability Letters, 83, 1863–1870. doi: 10.1016/j.spl.2013.04.017
   Web of Science ®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. doi: 10.1016/j.jmva.2010.05.010
   Web of Science ®Google Scholar
• Laib, N., and Louani, D. (2011), ‘Rates of Strong Consistencies of the Regression Function Estimator for Functional Stationary Ergodic Data’, Jounal of Statistical Planning and Inference, 141, 359–372. doi: 10.1016/j.jspi.2010.06.009
   Web of Science ®Google Scholar
• Laloë, T. (2008), ‘A k-Nearest Neighbor Approach for Functional Regression’, Statistics and Probability Letters, 78(10), 1189–1193. doi: 10.1016/j.spl.2007.11.014
   Web of Science ®Google Scholar
• Ling, N., Aneiros, G., and Vieu, P. (2017), ‘kNN Estimation in Functional Partial Linear Modeling’, Statistical Papers, in print.
   PubMed Web of Science ®Google Scholar
• Ling, N., and Vieu, P. (2018), ‘Nonparametric Modelling for Functional Data : Selected Survey and Tracks for Future’, Statistics. doi:10.1080/02331888.2018.1487120.
   PubMed Web of Science ®Google Scholar
• Ling, N.X., Wang, C., and Ling, J. (2016), ‘Modified Kernel Regression Estimation with Functional Time Series Data’, Statistics and Probability Letters, 114, 78–85. doi: 10.1016/j.spl.2016.03.009
   Web of Science ®Google Scholar
• Ling, N.X., and Wu, Y.H. (2012), ‘Consistency of Modified Kernel Regression Estimation for Functional Data’, Statistics, 46(2), 149–158. doi: 10.1080/02331888.2010.500077
   Web of Science ®Google Scholar
• Masry, E. (2005), ‘Nonparametric Regression Estimation for Dependent Functional Data: Asymptotic Normality’, Stochastic Processes and their Applications, 115, 155–177. doi: 10.1016/j.spa.2004.07.006
   Web of Science ®Google Scholar
• Müller, S., and Dippon, J. (2011), ‘k-NN Kernel Estimate for Nonparametric Functional Regression in Time Series Analysis’, www. mathematik.uni-stuttgart.de/preprints/downloads/2011/2011-014.pdf.
   Google Scholar
• Rachdi, M., and Vieu, P. (2007), ‘Nonparametric Regression for Functional Data: Automatic Smoothing Parameter Selection’, Jounal of Statistical Planning and Inference, 137(9), 2784–2801. doi: 10.1016/j.jspi.2006.10.001
   Web of Science ®Google Scholar
• Vieu, P. (2018), ‘On Dimension Reduction Models for Functional Data’, Statistics and Probability Letters, 136, 134–138. doi: 10.1016/j.spl.2018.02.032
   Web of Science ®Google Scholar