B. Présentation-générale-références-abdous and R. Theodorescu, Note on the geometric quantile of a random vector, Statistics and Probability Letters, vol.13, pp.333-336, 1992.

G. J. Babu and C. R. Rao, Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population, Journal of Multivariate Analysis, vol.27, issue.1, pp.15-23, 1988.
DOI : 10.1016/0047-259X(88)90112-1

R. R. Bahadur, A Note on Quantiles in Large Samples, The Annals of Mathematical Statistics, vol.37, issue.3, pp.577-580, 1966.
DOI : 10.1214/aoms/1177699450

V. Barnett, The Ordering of Multivariate Data, Journal of the Royal Statistical Society. Series A (General), vol.139, issue.3, pp.318-354, 1976.
DOI : 10.2307/2344839

F. K. Bedall and H. Zimmermann, Algorithm AS 143: The Mediancentre, Applied Statistics, vol.28, issue.3, pp.325-328, 1979.
DOI : 10.2307/2347218

Y. G. Berger and C. J. Et-skinner, A jackknife variance estimator for unequal probability sampling, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.15, issue.1, pp.79-89, 2005.
DOI : 10.1016/S0378-3758(98)00107-4

D. A. Binder, On the Variances of Asymptotically Normal Estimators from Complex Surveys, International Statistical Review / Revue Internationale de Statistique, vol.51, issue.3, pp.279-292, 1983.
DOI : 10.2307/1402588

B. M. Brown, Statistical use of the spatial median, Journal of the Royal Statistical Society, Ser. B, vol.45, pp.25-30, 1983.

B. M. Brown and T. P. Hettmansperger, Affine invariant rank methods in the bivariate location model, Journal of the Royal Statistical Society, Ser. B, vol.49, pp.301-310, 1987.

B. M. Brown and T. P. Hettmansperger, An affine invariant bivariate version of the sign test, Journal of the Royal Statistical Society, Ser. B, vol.51, pp.117-125, 1989.

H. Cardot, Conditional Functional Principal Components Analysis, Scandinavian Journal of Statistics, vol.57, issue.2, pp.317-335, 2007.
DOI : 10.1016/0047-259X(76)90001-4
URL : https://hal.archives-ouvertes.fr/hal-00004472

B. Chakraborty, On affine equivariant multivariate quantiles. The Institute of Statistical Mathematics, pp.380-403, 2001.

P. Chaudhuri, Multivariate location estimation using extension of R-estimates through U -statistics type approach. The Annals of Statistics, pp.897-916, 1992.

P. Chaudhuri and D. Sengupta, Sign Tests in Multidimension: Inference Based on the Geometry of the Data Cloud, Journal of the American Statistical Association, vol.48, issue.424, pp.1363-1370, 1993.
DOI : 10.1080/01621459.1993.10476419

P. Chaudhuri, On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, vol.24, issue.434, pp.862-872, 1996.
DOI : 10.1080/01621459.1996.10476954

Y. Cheng, D. Gooijer, and J. , On the uth geometric conditional quantile, Journal of Statistical Planning and Inference, vol.137, issue.6, pp.1914-1930, 2007.
DOI : 10.1016/j.jspi.2006.02.014

G. Collomb, W. H?rdle, and S. Hassani, A note on prediction via estimation of the conditional mode function, Journal of Statistical Planning and Inference, vol.15, pp.227-236, 1987.
DOI : 10.1016/0378-3758(86)90099-6

J. Dauxois, A. Pousse, R. , and Y. , Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference, Journal of Multivariate Analysis, vol.12, issue.1, pp.136-154, 1982.
DOI : 10.1016/0047-259X(82)90088-4

D. Gooijer, J. G. Gannoun, A. Et-zerom, and D. , A Multivariate Quantile Predictor, Communications in Statistics - Theory and Methods, vol.35, issue.1, pp.133-147, 2006.
DOI : 10.2307/2669619
URL : https://hal.archives-ouvertes.fr/hal-01125201

A. Dessertaine, Sondage et séries temporelles : une application pour la prévision de la consommation électrique, 2006.

J. C. Deville, Variance estimation for complex statistics and estimators : linearization and residual techniques, Survey Methodology, vol.25, pp.193-203, 1999.

D. L. Donoho and M. Gasko, Breakdown properties of location estimates based on halfspace depth and projected outlyingness. The Annals of Statistics, pp.1803-1827, 1992.

P. Doukhan, Mixing : Properties and Examples, Lecture Notes in Statistics, vol.85, 1994.

W. F. Eddy, Convex Hull Peeling. COMPSTAT 1982 for IASC, pp.42-47, 1982.
DOI : 10.1007/978-3-642-51461-6_4

W. F. Eddy and . Billard, Ordering of Multivariate Data Computer Science and Statistics : The Interface, pp.25-30, 1985.

T. Ferguson, Mathematical Statistics : A Decision Theoric Approach, 1967.

A. Gannoun, J. Saracco, A. Yan, and G. E. Bonney, On Adaptive Transformation???Retransformation Estimate of Conditional Spatial Median, Communications in Statistics - Theory and Methods, vol.35, issue.10, pp.1981-2011, 2003.
DOI : 10.2307/2669619

J. C. Gower, Algorithm AS 78: The Mediancentre, Applied Statistics, vol.23, issue.3, pp.466-470, 1974.
DOI : 10.2307/2347150

J. B. Haldane, Note on the median of a multivariate distribution, Biometrika, vol.35, issue.3-4, pp.414-415, 1948.
DOI : 10.1093/biomet/35.3-4.414

C. I. Isaki and W. A. Fuller, Survey Design under the Regression Superpopulation Model, Journal of the American Statistical Association, vol.38, issue.377, pp.89-96, 1982.
DOI : 10.1080/01621459.1982.10477770

T. Kato, Perturbation theory for linear operators, 1966.
DOI : 10.1007/978-3-662-12678-3

J. H. Kemperman, The median of a finite measure on a Banach space In Statistical Data Analysis based on the L 1 -norm and related methods, pp.217-230, 1987.

S. J. Kim, A metrically trimmed mean as a robust estimator of location. The annals of Statistics, pp.1534-1547, 1992.

R. Koenker and G. Basset, Regression Quantiles, Econometrica, vol.46, issue.1, pp.33-50, 1978.
DOI : 10.2307/1913643

P. Kokic, J. Breckling, and O. Lübke, A new definition of multivariate M quantiles . Statistical data analysis based on the L 1 -norm and related methods, 2002.

. Stat and . Ind, Technol. : Statistical Data Analysis, pp.15-24

V. Koltchinskii, M-estimation, convexity and quantiles. The Annals of Statistics, pp.435-477, 1997.
DOI : 10.1214/aos/1031833659

M. S. Kovacevic and D. A. Et-binder, ÊVariance estimation for measures of income inequality and polarizationÊ, Journal of Official Statistics, vol.13, issue.1, pp.41-58, 1997.

R. Y. Liu, J. M. Parelius, and K. Singh, Multivariate analysis by data depth : descriptive statistics, graphics and inference (with discussion) The Annals of Statistics, pp.783-858, 1999.

H. Oja, Descriptive statistics for multivariate distributions, Statistics & Probability Letters, vol.1, issue.6, pp.327-332, 1983.
DOI : 10.1016/0167-7152(83)90054-8

J. O. Ramsay and B. W. Silverman, Applied Functional Data Analysis : Methods and Case Studies, 2002.
DOI : 10.1007/b98886

J. N. Rao, C. F. Wu, and K. Et-yue, Some recent work on resampling methods for complex surveys, Survey Methodology, vol.18, pp.209-217, 1992.

M. Rosenblatt, A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION, Proc. Nat. Acad. Sci, pp.43-47, 1956.
DOI : 10.1073/pnas.42.1.43

C. E. Särndal, B. Swensson, and J. Wretman, Model Assisted Survey Sampling, 1992.
DOI : 10.1007/978-1-4612-4378-6

D. E. Scates, Locating the median of the population in the United States, Metron, vol.11, pp.49-66, 1933.

C. G. Small, A Survey of Multidimensional Medians, International Statistical Review / Revue Internationale de Statistique, vol.58, issue.3, pp.263-277, 1990.
DOI : 10.2307/1403809

R. Serfling, Quantile functions for multivariate analysis: approaches and applications, Statistica Neerlandica, vol.28, issue.2, pp.214-232, 2002.
DOI : 10.1006/jmva.1999.1894

C. J. Skinner, D. J. Holmes, and T. M. Smith, The Effect of Sample Design on Principal Component Analysis, Journal of the American Statistical Association, vol.63, issue.395, pp.789-798, 1986.
DOI : 10.1080/01621459.1981.10477604

Y. Tillé, Th?orie des sondages : Échantillonnage et estimation en populations finies : cours et exercices, 2001.

Y. Vardi and C. H. Et-zhang, The multivariate L1-median and associated data depth, Proceedings of the National Academy of Sciences, vol.97, issue.4, pp.1423-1426, 2000.
DOI : 10.1073/pnas.97.4.1423

A. Weber, Über den standard der industrien, Tubingen, English translation by Alfred Weber's theory of location of industies, 1909.

Y. Zuo and R. Serfling, General notions of statistical depth function. The Annals of Statistics, pp.461-482, 2000.

F. K. Bedall and H. Zimmermann, Algorithm AS 143: The Mediancentre, Algorithm AS 143, the Mediancenter, pp.325-328, 1979.
DOI : 10.2307/2347218

F. J. Breidt and J. Opsomer, Local Polynomial Regression Estimators in Survey Sampling, The Annals of Statistics, pp.1026-1053, 2000.

P. Chaudhuri, On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, vol.24, issue.434, pp.862-872, 1996.
DOI : 10.1080/01621459.1996.10476954

B. Chakraborty, On affine equivariant multivariate quantiles, The Institute of Statistical Mathematics, pp.80-403, 2001.

J. G. De-gooijer, A. Gannoun, and D. Zerom, A Multivariate Quantile Predictor, Communications in Statistics - Theory and Methods, vol.35, issue.1, pp.133-147, 2006.
DOI : 10.2307/2669619
URL : https://hal.archives-ouvertes.fr/hal-01125201

J. C. Deville, Variance estimation for complex statistics and estimators : linearization and residual techniques, Survey Methodology, vol.25, pp.193-203, 1999.

T. Ferguson, Mathematical Statistics : A Decision Theoric Approach, 1967.

C. A. Francisco and W. A. Fuller, Quantile Estimation with a Complex Survey Design, The Annals of Statistics, vol.19, issue.1, pp.454-469, 1991.
DOI : 10.1214/aos/1176347993

C. Gini and L. Galvani, Di talune estensioni dei concetti di media ai caratteri qualitativi, Journal of the American Statistical Association, vol.25, pp.448-450, 1929.

V. P. Godambe and M. E. Thompson, Parameters of Superpopulation and Survey Population: Their Relationships and Estimation, International Statistical Review / Revue Internationale de Statistique, vol.54, issue.2, pp.127-138, 1986.
DOI : 10.2307/1403139

J. B. Haldane, Note on the median of a multivariate distribution, Biometrika, vol.35, issue.3-4, pp.414-415, 1948.
DOI : 10.1093/biomet/35.3-4.414

D. G. Horvitz and D. J. Thompson, A Generalization of Sampling Without Replacement from a Finite Universe, Journal of the American Statistical Association, vol.1, issue.260, pp.663-685, 1952.
DOI : 10.1080/01621459.1949.10483288

R. Koenker and G. Basset, Regression Quantiles, Regression Qantiles, pp.33-50, 1978.
DOI : 10.2307/1913643

. Kuk, Estimation of distribution functions and medians under sampling with unequal probabilities, Biometrika, vol.75, issue.1, pp.97-103
DOI : 10.1093/biomet/75.1.97

J. H. Kemperman, The median of a finite measure on a Banach space, Statistical Data Analysis Based on the L 1 Norm and Related Methods, pp.217-230, 1987.

G. M. Reaven and R. G. Miller, An attempt to define the nature of chemical diabetes using a multidimensional analysis, Diabetologia, vol.13, issue.1, pp.17-24, 1979.
DOI : 10.1007/BF00423145

C. E. Särndal, On ?-inverse weighting versus best linear unbiased weighting in probability sampling, Biometrika, vol.67, pp.639-650, 1980.

R. Serfling, Quantile functions for multivariate analysis: approaches and applications, Statistica Neerlandica, vol.28, issue.2, pp.214-232, 2002.
DOI : 10.1006/jmva.1999.1894

C. G. Small, A Survey of Multidimensional Medians, International Statistical Review / Revue Internationale de Statistique, vol.58, issue.3, pp.263-277, 1990.
DOI : 10.2307/1403809

R. Berger, Y. G. Skinner, and C. J. , A jackknife variance estimator for unequal probability sampling, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.15, issue.1, pp.79-89, 2005.
DOI : 10.1016/S0378-3758(98)00107-4

P. Besse, R. , and J. O. , Principal components analysis of sampled functions, Psychometrika, vol.78, issue.A, pp.285-311, 1986.
DOI : 10.1007/BF02293986

P. C. Besse, H. Cardot, and D. B. Stephenson, Autoregressive Forecasting of Some Functional Climatic Variations, Scandinavian Journal of Statistics, vol.27, issue.4, pp.673-687, 2000.
DOI : 10.1111/1467-9469.00215

D. Bosq, Linear Processes in Function Spaces, Lecture Notes in Statistics, vol.149, 2000.
DOI : 10.1007/978-1-4612-1154-9

F. J. Breidt and J. D. Opsomer, Local Polynomial Survey Regression Estimators in Survey Sampling, The Annals of Statistics, vol.4, pp.1026-1053, 2000.

C. Campbell and A. D. Little, A Different View of Finite Population Estimation, Proceeding of the Section on Survey Research Methods, pp.319-324, 1980.

H. Cardot, Nonparametric estimation of smoothed principal components analysis of sampled noisy functions, Journal of Nonparametric Statistics, vol.53, issue.4, pp.503-538, 2000.
DOI : 10.1214/aos/1033066196

H. Cardot, R. Faivre, and M. Goulard, Functional approaches for predicting land use with the temporal evolution of coarse resolution remote sensing data, Journal of Applied Statistics, vol.43, issue.10, pp.1185-1199, 2003.
DOI : 10.1016/0034-4257(79)90013-0

P. Castro, W. Lawton, and E. Sylvestre, Principal Modes of Variation for Processes with Continuous Sample Curves, Technometrics, vol.28, issue.4, pp.329-337, 1986.
DOI : 10.2307/1268982

F. Chatelin and G. Hébrail, Spectral approximation of linear operators Generic tool for summarizing distributed data streams, 1983.

J. M. Chiou, H. G. Müller, J. L. Wang, and J. R. Carey, A functional multiplicative effects model for longitudinal data, with application to reproductive histories of female medflies, Statist. Sinica, vol.13, pp.1119-1133, 2003.

C. Croux and A. Ruiz-gazen, High breakdown estimators for principal components: the projection-pursuit approach revisited, Journal of Multivariate Analysis, vol.95, issue.1, pp.206-226, 2005.
DOI : 10.1016/j.jmva.2004.08.002

A. Cuevas, M. Febrero, and R. Fraiman, Linear functional regression: The case of fixed design and functional response, Canadian Journal of Statistics, vol.6, issue.2, pp.285-300, 2002.
DOI : 10.2307/3315952

A. Dessertaine, Sondage et séries temporelles : une application pour la prévision de la consommation électrique, 2006.

J. C. Deville, M??thodes statistiques et num??riques de l'analyse harmonique, Annales de l'ins????, vol.15, issue.15, pp.3-104, 1974.
DOI : 10.2307/20075177

J. C. Deville, Variance estimation for complex statistics and estimators : linearization and residual techniques, Survey Methodology, vol.25, pp.193-203, 1999.

F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis, Theory and Applications, 2006.

F. R. Hampel, The Influence Curve and its Role in Robust Estimation, Journal of the American Statistical Association, vol.15, issue.4, pp.383-393, 1974.
DOI : 10.1214/aoms/1177730385

T. Hastie and C. Mallows, [A Statistical View of Some Chemometrics Regression Tools]: Discussion, Technometrics, vol.35, issue.2, pp.140-143, 1993.
DOI : 10.2307/1269658

C. T. Isaki and W. A. Fuller, Survey Design under the Regression Superpopulation Model, Journal of the American Statistical Association, vol.38, issue.377, pp.89-96, 1982.
DOI : 10.1080/01621459.1982.10477770

G. James, T. Hastie, and C. Sugar, Principal component models for sparse functional data, Biometrika, vol.87, issue.3, pp.587-602, 2000.
DOI : 10.1093/biomet/87.3.587

T. Kato, Perturbation theory for linear operators, 1966.

M. Kirkpatrick and N. Heckman, A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters, Journal of Mathematical Biology, vol.111, issue.4, pp.429-450, 1989.
DOI : 10.1007/BF00290638

A. Kneip and K. J. Utikal, Inference for Density Families Using Functional Principal Component Analysis, Journal of the American Statistical Association, vol.96, issue.454, pp.519-542, 2001.
DOI : 10.1198/016214501753168235

R. Mises, On the Asymptotic Distribution of Differentiable Statistical Functions, The Annals of Mathematical Statistics, vol.18, issue.3, pp.309-348, 1947.
DOI : 10.1214/aoms/1177730385

J. O. Ramsay and B. W. Silverman, Applied Functional Data Analysis : Methods and Case Studies, 2002.
DOI : 10.1007/b98886

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2005.

P. M. Robinson and C. E. Särndal, Asymptotic properties of the generalized regression estimator in probability sampling, Sankhya : The Indian Journal of Statistics, vol.45, pp.240-248, 1983.

R. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

B. W. Silverman, Smoothed functional principal components analysis by choice of norm, The Annals of Statistics, vol.24, issue.1, pp.1-24, 1996.
DOI : 10.1214/aos/1033066196

B. Abdous and R. Theodorescu, Note on the spatial quantile of a random vector, Statistics & Probability Letters, vol.13, issue.4, pp.333-336, 1992.
DOI : 10.1016/0167-7152(92)90043-5

A. Berlinet, B. Cadre, and A. Gannoun, -median and its estimation, Journal of Nonparametric Statistics, vol.73, issue.5, pp.631-645, 2001.
DOI : 10.2307/1403809
URL : https://hal.archives-ouvertes.fr/hal-00459437

A. Berlinet, B. Cadre, and A. Gannoun, Estimation of conditional L1-median from dependent observations, Statistics & Probability Letters, vol.55, issue.4, pp.353-358, 2001.
DOI : 10.1016/S0167-7152(01)00046-3

A. Berlinet, A. Gannoun, and E. Matzner-l£ber, Asymptotic normality of convergent estimates of conditional quantiles, Statistics, vol.1, issue.2, pp.139-169, 2001.
DOI : 10.1214/aos/1176348513

D. Bosq and J. P. Lecoutre, Théorie de l'estimation fonctionnelle, Economica, 1987.

B. M. Brown and T. P. Hettmansperger, Affine Invariant Rank Methods in the Bivariate Location Model, Journal of the Royal Statistical Society, Ser. B, vol.49, pp.301-310, 1987.

B. M. Brown and T. P. Hettmansperger, An Affine Invariant Bivariate Versions of the Sign Test, Journal of the Royal Statistical Society, Ser. B, vol.51, pp.117-125, 1989.

P. Chaudhuri, On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, vol.24, issue.434, pp.862-872, 1996.
DOI : 10.1080/01621459.1996.10476954

M. Chaouch, A. Gannoun, and J. Saracco, Quantile geometric conditionnel et non conditionnel : une méthode d'estimation et son implementation en R, 2007.

B. Chakraborty, On affine equivariant multivariate quantiles. The Institute of Statistical Mathematics, pp.380-403, 2001.

Y. Cheng, D. Gooijer, and J. , On the uth geometric conditional quantile, Journal of Statistical Planning and Inference, vol.137, issue.6, pp.1914-1930, 2007.
DOI : 10.1016/j.jspi.2006.02.014

J. De-gooijer, A. Gannoun, and D. Zerom, A Multivariate Quantile Predictor, Communications in Statistics - Theory and Methods, vol.35, issue.1, pp.133-147, 2002.
DOI : 10.2307/2669619
URL : https://hal.archives-ouvertes.fr/hal-01125201

P. Doukhan, Mixing : Properties and Examples, Lecture Notes in Statistics, vol.85, 1994.

W. F. Eddy, Convex Hull Peeling. COMPSTAT 1982 for IASC, pp.42-47, 1982.

W. F. Eddy, Set Valued Ordering of Bivariate Data, Stochastics Geometry, Geometric Statistics and Stereology, pp.79-90, 1983.

W. F. Eddy and . Billard, Ordering of Multivariate Data Computer Science and Statistics : The Interface, pp.25-30, 1985.

T. Ferguson, Mathematical Statistics : A Decision Theoric Approach, 1967.

J. H. Kemperman, The median of a finite measure on a Banach space In Statistical Data Analysis based on the L 1 -norm and related methods, pp.217-230, 1987.

H. Oja, Descriptive statistics for multivariate distributions, Statistics & Probability Letters, vol.1, issue.6, pp.327-332, 1983.
DOI : 10.1016/0167-7152(83)90054-8

M. Rosenblatt, A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION, Proc. Nat. Acad. Sci, pp.43-47, 1956.
DOI : 10.1073/pnas.42.1.43

R. Serfling, Quantile functions for multivariate analysis: approaches and applications, Statistica Neerlandica, vol.28, issue.2, pp.214-232, 2002.
DOI : 10.1006/jmva.1999.1894

R. Serfling, Nonparametric multivariate descriptive measures based on spatial quantiles, Journal of Statistical Planning and Inference, vol.123, issue.2, pp.259-278, 2004.
DOI : 10.1016/S0378-3758(03)00156-3

#. Plan and S. ############################-sas-=-function, ### ENTREE ### Xpop une matrice Npop ligne p colonnes: les lignes sont les indivudus (courbe) et les colonne ### sont les point de d?scritisation de mes courbes ### n la taille de l'?chantillon ? tirer de la popuation ### n.sim est le nombre de simulation ### SORTIE ### mu.est l'estimateur de la fonction moyenne ### vecp1.varest l'estimateur de la variance du premier vecteur propre ### valp.est les estimateurs des n valeurs propres ### valp.varest l'estimateur de la variance des valeurs propres ### vecp1

. Mat, indech = matrix(NA,ncol=n.sim,nrow=n) for (i in 1:n.sim){ Mat.indech[,i] = sort(sample(ind

N. Gamma and .. , sim)) vecp1.varest = Gamma.est valp.est = matrix(NA,ncol=2,nrow=n.sim) valp.varest = matrix(NA,ncol=2,nrow=n.sim) vecp1.est = matrix(NA,ncol=p,nrow=n.sim) vecp2.est = matrix(NA,ncol=p,nrow=n.sim) for (i in 1:n.sim){ Xsample = Xpop, ### Sauvegarde des resultats des simulations mu.est = matrix le nuage des 20 observations sur lequel chaque segment représente le vecteur normé S(??Y i ) qui relie une observation i au quantile géométrique Q(u) ( qui est le point représenté par un triangle et situé en bas à droite). A gauche, le vecteur u (trait continu) est la moyenne des vecteurs unitaires S(? ? Y i ) (tracés en pointillés), p.37