It is well known that robust estimation provides an alternative approach to classical methods which is not unduly afiected by the presence of outliers. Recently, these robust estimators have been considered for models with functional data. In this talk, we focus on asymptotic properties of a conditional nonparametric estimation of a real valued variable with a functional covariate. We present results dealing with convergence in probability, asymptotic normality and Lqerrors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Attouch, A. Laksaci. and E. Ould-Sa.:ïd. Asymptotic distribution of robust esti-mator for functional nonparametric models, Prépublication, LMPA No 314 Janvier (2007). Submitted.
N. Azzeddine, A. Laksaci, E. Ould-Sa.:ïd. On the robust nonparametric regression estimation for functional regressor, Statist. and Probab. Lett. (2007), Accepted under minor revision.
P. Besse, H. Cardot and F. Ferraty.: Simultaneous nonparametric regressions of unbalanced longitudinal data. Comput. Statist. Data Anal. 24, 255-270 (1997).
G. Boente, R. Fraiman.: Asymptotic distribution of robust estimators for nonpara-metric models from mixing processes. Ann. Statist. 18, 891-906 (1990).
B. Cadre.: Convergent estimators for the L1 -median of a Banach valued random variable. Statistics. 35, 509-521 (2001).
H. Cardot, C. Crambes, P. Sarda.: Quantiles regression when the covariates are functions. J. of Nonparam. Stat. 17, 841-856 (2005).
G. Collomb, W. Härdle.: Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stoch. Proc. Appl. 23, 77-89 (1986).
L. Delsol.: Régression non-paramétrique fonctionnelle: Expressions asymptotiques des moments. (2007). Submitted.
F. Ferraty and P. Vieu.: The functional nonparametric model and application to spectrometric data. Comp. Statist. 17, 545-564 (2002).
F. Ferraty and P. Vieu.: Nonparametric functionnal data analysis. Springer-Verlag. New York. (2006).
P.J. Huber.: Robust estimation of a location parameter. Ann. of the Math. Statist. 35,73-101 (1964).
N. Laïb and E. Ould-Saïd.: A robust nonparametric estimation of the autoregression function under an ergodic hypothesis. Canad. J. Statist. 28, 817-828 (2000).
R. Robinson.: Robust Nonparametric Autoregression. Lecture Notes in Statistics, Springer-Verlag. New York. 26, 247-255 (1984).
J. Ramsay and B.W. Silverman.: Applied functional data analysis. Springer-Verlag, New York. (2002).
J. Ramsay and B.W. Silverman.: Functional data analysis (Sec. Ed.). Springer-Verlag, New York. (2005).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Physica-Verlag Heidelberg
About this paper
Cite this paper
Crambes, C., Delsol, L., Laksaci, A. (2008). Robust Nonparametric Estimation for Functional Data. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2062-1_18
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2061-4
Online ISBN: 978-3-7908-2062-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)