Asymptotic normality of locally modelled regression estimator for functional data

References

• Amiri, A., Crambes, C., and Thiam, B. (2014), ‘Recursive Estimation of Nonparametric Regression with Functional Covariate’, Computational Statistics & Data Analysis, 69, 154–172. doi: 10.1016/j.csda.2013.07.030
   Web of Science ®Google Scholar
• Aneiros-Prez, G., and Vieu, P. (2006), ‘Semi-Functional Partial Linear Regression’, Statistics & Probability Letters, 76, 1102–1110. doi: 10.1016/j.spl.2005.12.007
   Web of Science ®Google Scholar
• Baíllo, A., and Grané, A. (2009), ‘Local Linear Regression for Functional Predictor and Scalar Response’, Journal of Multivariate Analysis, 100, 102–111. doi: 10.1016/j.jmva.2008.03.008
   Web of Science ®Google Scholar
• Barrientos-Marin, J., Ferraty, F., and Vieu, P. (2010), ‘Locally Modelled Regression and Functional Data’, Journal of Nonparametric Statistics, 22, 617–632. doi: 10.1080/10485250903089930
   Web of Science ®Google Scholar
• Benhenni, K., Hedli-Griche, S., Rachdi, M., and Vieu, P. (2008), ‘Consistency of The Regression Estimator with Functional Data Under Long Memory Conditions’, Statistics & Probability Letters, 78, 1043–1049. doi: 10.1016/j.spl.2007.11.011
   Web of Science ®Google Scholar
• Berlinet, A., Elamine, A., and Mas, A. (2011), ‘Local Linear Regression for Functional Data’, Annals of the Institute of Statistical Mathematics, 63, 1047–1075. doi: 10.1007/s10463-010-0275-8
   Web of Science ®Google Scholar
• Boj, E., Delicado, P., and Fortiana, J. (2010), ‘Distance-Based Local Linear Regression for Functional Predictors’, Computational Statistics & Data Analysis, 54, 429–437. doi: 10.1016/j.csda.2009.09.010
   Web of Science ®Google Scholar
• Bongiorno, E. G., Salinelli, E., Goia, A., and Vieu, P. (2014), Contributions in infinite-dimensional statistics and related topics, Società Editrice Esculapio.
   Google Scholar
• Bosq, D. (2000), Linear Processes in Function Spaces: Theory and Applications (Vol. 149), Springer.
   Google Scholar
• Burba, F., Ferraty, F., and Vieu, P. (2009), ‘k-Nearest Neighbour Method in Functional Nonparametric Regression’, Journal of Nonparametric Statistics, 21, 453–469. doi: 10.1080/10485250802668909
   Web of Science ®Google Scholar
• Chen, D., Hall, P., and Müller H.-G. (2011), ‘Single and Multiple Index Functional Regression Models with Nonparametric Link’, Annals of Statistics, 39, 1720–1747. doi: 10.1214/11-AOS882
   Web of Science ®Google Scholar
• Delsol, L. (2009), ‘Advances on Asymptotic Normality in Non-Parametric Functional time Series Analysis’, Statistics, 43, 13–33. doi: 10.1080/02331880802184961
   Web of Science ®Google Scholar
• Demongeot, J., Laksaci, A., Madani, F., and Rachdi, M. (2013), ‘Functional Data: Local Linear Estimation of the Conditional Density and Its Application’, Statistics, 47, 26–44. doi: 10.1080/02331888.2011.568117
   Web of Science ®Google Scholar
• Demongeot, J., Laksaci, A., Rachdi, M., and Rahmani, S. (2014), ‘On The Local Linear Modelization of The Conditional Distribution for Functional Data’, Sankhya A, 76, 328–355. doi: 10.1007/s13171-013-0050-z
   Google Scholar
• Ezzahrioui, M.H., and Ould-Said, E. (2008), ‘Asymptotic Normality of A Nonparametric Estimator of the Conditional Mode Function for Functional Data’, Journal of Nonparametric Statistics, 20, 3–18. doi: 10.1080/10485250701541454
   Web of Science ®Google Scholar
• Fan, J. (1992), ‘Design-Adaptive Nonparametric Regression’, Journal of the American Statistical Association, 87, 998–1004. doi: 10.1080/01621459.1992.10476255
   Web of Science ®Google Scholar
• Fan, J., and Yao, Q. (2003), Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag.
   Google Scholar
• Ferraty, F., Laksaci, A., Tadj, A., and Vieu, P. (2010), ‘Rate of Uniform Consistency for Nonparametric Estimates with Functional Variables’, Journal of Statistical Planning and Inference, 140(2):335–352. doi: 10.1016/j.jspi.2009.07.019
   Web of Science ®Google Scholar
• Ferraty, F., Laksaci, A., Tadj, A., and Vieu, P. (2011), ‘Kernel Regression with Functional Response’, Electronic Journal of Statistics, 5, 159–171. doi: 10.1214/11-EJS600
   Web of Science ®Google Scholar
• Ferraty, F., Mas, A., and Vieu, P. (2007), ‘Nonparametric Regression on Functional Data: Inference and Practical Aspects’, Australian & New Zealand Journal of Statistics, 49, 267–286. doi: 10.1111/j.1467-842X.2007.00480.x
   Web of Science ®Google Scholar
• Ferraty, F., Van Keilegom, I., and Vieu, P. (2012), ‘Regression when Both Response and Predictor are Functions’, Journal of Multivariate Analysis, 109, 10–28. doi: 10.1016/j.jmva.2012.02.008
   Web of Science ®Google Scholar
• Ferraty, F., and Vieu, P. (2004), ‘Nonparametric Models for Functional Data, with Application in Regression, Time Series Prediction and Curve Discrimination’, Journal of Nonparametric Statistics, 16, 111–125. doi: 10.1080/10485250310001622686
   Web of Science ®Google Scholar
• Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics), New York: Springer-Verlag.
   Google Scholar
• Goia, A., and Vieu, P. (2014), ‘A Partitioned Single Functional Index Model’, Computational Statistics, 1–20.
   Google Scholar
• Horváth, L., and Kokoszka, P.. (2012), Inference for Functional Data with Applications, New York: Springer.
   Google Scholar
• Kudraszow, N. L., and Vieu, P. (2013), ‘Uniform Consistency of kNN Regressors for Functional Variables’, Statistics & 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, 2266–2281. doi: 10.1016/j.jmva.2010.05.010
   Web of Science ®Google Scholar
• Lian, H. (2012), ‘Empirical Likelihood Confidence Intervals for Nonparametric Functional Data Analysis’, Journal of Statistical Planning and Inference, 142, 1669–1677. doi: 10.1016/j.jspi.2012.02.008
   Web of Science ®Google Scholar
• Ling, N., Liang, L., and Vieu, P. (2015), ‘Nonparametric Regression Estimation for Functional Stationary Ergodic Data with Missing At Random’, Journal of Statistical Planning and Inference, 162, 75–87. doi: 10.1016/j.jspi.2015.02.001
   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
• Messaci, F., Nemouchi, N., Ouassou, I., and Rachdi, M. (2015), ‘Local Polynomial Modelling of the Conditional Quantile for Functional Data’, Statistical Methods & Applications, 1–26.
   Google Scholar
• Owen, A. (1990), ‘Empirical Likelihood Ratio Confidence Regions’, Annals of Statistics, 18, 90–120. doi: 10.1214/aos/1176347494
   Web of Science ®Google Scholar
• Owen, A.B. (1988), ‘Empirical Likelihood Ratio Confidence Intervals for a Single Functional’, Biometrika, 75, 237–249. doi: 10.1093/biomet/75.2.237
   Web of Science ®Google Scholar
• Qin, J., and Lawless, J. (1994), ‘Empirical Likelihood and General Estimating Equations’, Annals of Statistics, 22, 300–325. doi: 10.1214/aos/1176325370
   Web of Science ®Google Scholar
• Rachdi, M., Laksaci, A., Demongeot, J., Abdali, A., and Madani, F. (2014), ‘Theoretical and Practical Aspects of the Quadratic Error in the Local Linear Estimation of the Conditional Density for Functional Data’, Computational Statistics & Data Analysis, 73, 53–68. doi: 10.1016/j.csda.2013.11.011
   Web of Science ®Google Scholar
• Rachdi, M., and Vieu, P. (2007), ‘Nonparametric Regression for Functional Data: Automatic Smoothing Parameter Selection’, Journal of Statistical Planning and Inference, 137, 2784–2801. doi: 10.1016/j.jspi.2006.10.001
   Web of Science ®Google Scholar
• Ramsay, J., and Silverman, B.W. (2005), Functional Data Analysis (2nd ed.), New York: Springer-Verlag.
   Google Scholar
• Xiong, X. Z., and Lin, Z. Y. (2013), ‘Empirical Likelihood Inference for Nonparametric Regression Functions with Functional Stationary Ergodic Data’, Communications in Statistics-Theory and Methods, 42, 3421–3431. doi: 10.1080/03610926.2011.630766
   Web of Science ®Google Scholar