Advanced SearchSearch Tips
Nonparametric M-Estimation for Functional Spatial Data
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Nonparametric M-Estimation for Functional Spatial Data
Attouch, Mohammed Kadi; Chouaf, Benamar; Laksaci, Ali;
  PDF(new window)
This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider , be a -valued measurable strictly stationary spatial process, where is a semi-metric space and we study the spatial interaction of and via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.
Asymptotic distribution;spatial data;functional data;kernel estimate;nonparametric model;robust estimation;small balls probability;
 Cited by
Anselin, L. and Florax, R. J. G. M. (1995). New Directions in Spatial Econometrics, Springer, Berlin.

Attouch, M. K., Laksaci, A. and Ould Said, E. (2009). Asymptotic distribution of robust estimator for functional nonparametric models, Communications in Statistics - Theory and Methods, 38, 1317-1335. crossref(new window)

Attouch, M. K., Laksaci, A. and Ould-Said, E. (2010). Asymptotic normality of a robust estimator of the regression function for functional time series, Journal of the Korean Statistical Society, 39, 489-500. crossref(new window)

Azzedine, N., Laksaci, A. and Ould Said, E. (2008). On the robust nonparametric regression estimation for functional regressor, Statistics & Probability Letters, 78, 3216-3221. crossref(new window)

Biau, G. (2003). Spatial Kernel Density Estimation, Mathematical Methods of Statistics, 12, 371-390.

Biau, G. and Cadre, B. (2004). Nonparametric spatial prediction, Statistical Inference for Stochastic Processes, 7, 327-349. crossref(new window)

Boente, G. and Fraiman, R. (1989). Nonparametric regression estimation, Journal of Multivariate Analysis, 29, 180-198. crossref(new window)

Bosq, D. (2000). Linear Processes in Function Spaces. Theory and Application, Lectures Notes in Statistics. Springer Verlag, New York.

Cadre, B. (2001). Convergent estimators for the $L_1$-median of a Banach-valued random variable, Statistics, 35, 509-521. crossref(new window)

Carbon, M., Francq, C. and Tran, L. T. (2007). Kernel regression estimation for random fields, Journal of Statistical Planning and Inference, 137, 778-798. crossref(new window)

Carbon, M., Hallin, M. and Tran, L. T. (1996). Kernel density estimation for random fields: The $L^1$ theory, Journal of Nonparametric Statistics, 6, 157-170. crossref(new window)

Chen, J. and Zhang, L. (2009). Asymptotic properties of nonparametric M-estimation for mixing functional data, Journal of Statistical Planning and Inference, 139, 533-546. crossref(new window)

Collomb, G. and Hardle, W. (1986). Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations, Stochastic Processes and their Applications, 23, 77-89. crossref(new window)

Crambes, C., Delsol, L. and Laksaci, A. (2008). Robust nonparametric estimation for functional data, Journal of Nonparametric Statistics, 20, 573-598. crossref(new window)

Cressie, N. A. C. (1991). Statistics for spatial Data, Wiley Series in Probability and Mathematical Statistics, New York.

Dabo-Niang, S. and Thiam, B. (2010). Robust quantile estimation and prediction for spatial processes, Statistics & Probability Letters, 80, 1447-1458. crossref(new window)

Dabo-Niang, S. and Yao, A. F. (2007). Spatial kernel regression estimation, Mathematical Methods of Statistics, 16, 1-20. crossref(new window)

Delicado, P., Giraldo, R., Comas, C. and Mateu, J. (2010). Statistics for spatial functional data: Some recent contributions, Environmetrics, 21, 224-239. crossref(new window)

Doukhan, P., Massart, P. and Rio, E. (1994). The functional central limit theorem for strongly mixing processes, Annales de l'Institut Henri Poincare, 30, 63-82.

Ferraty, F., Laksaci, A. and Vieu, P. (2006). Estimating some characteristics of the conditional distribution in nonparametric functional models, Statistical Inference for Stochastic Processes, 9, 47-76. crossref(new window)

Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis. Theory and Practice, Springer-Verlag, New York.

Gheriballah, A., Laksaci, A. and Rouane, R. (2010). Robust nonparametric estimation for spatial regression, Journal of Statistical Planning and Inference, 140, 1656-1670. crossref(new window)

Guyon, X. (1987). Estimation d'un champ par pseudo-vraisemblance conditionnelle: Etude asymptotique et application au cas Markovien, Proceedings of the Sixth Franco-Belgian Meeting of Statisticia.

Guyon, X. (1995). Random Fields on a Network - Modeling, Statistics, and Applications, Springer, New York.

Hallin, M., Lu, Z. and Yu, K. (2009). Local linear spatial quantile regression, Bernoulli, 15, 659-686. crossref(new window)

Laib, N. and Ould Said, E. (2000). A robust nonparametric estimation of the autoregression function under ergodic hypothesis, Canadian Journal of Statistics, 28, 817-828. crossref(new window)

Li, J. and Tran, L. T. (2009). Nonparametric estimation of conditional expectation, Journal of Statistical Planning and Inference, 139, 164-175. crossref(new window)

Lu, C., Chen, D. and Kou, Y. (2003). Detecting spatial outliers with multiple attributes, IEEE, 2-3, 122-128. crossref(new window)

Nerini, D., Monestiez, P. and Mante, C. (2010). A cokriging method for spatial functional, Journal of Multivariate Analysis, 101, 409-418. crossref(new window)

Ramsay, J. (2008). FDA problems that I like to talk about, Personal Communication.

Ramsay, J. O. and Silverman, B. W. (2002). Applied Functional Data Analysis. Methods and Case Studies, Springer-Verlag, New York.

Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, Second edition, Springer-Verlag, New York.

Ripley, B. (1981). Spatial Statistics, Wiley, New York.

Tran, L. T. (1990). Kernel density estimation under dependence, Statistics & Probability Letters, 10, 193-201. crossref(new window)

Xu, R. andWang, J. (2008). $L_1$- estimation for spatial nonparametric regression, Journal of Nonparametric Statistics, 20, 523-537. crossref(new window)