K. S. Alexander, The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes, The Annals of Probability, vol.15, issue.1, pp.178-203, 1987.
DOI : 10.1214/aop/1176992263

G. Bennett, Probability Inequalities for the Sum of Independent Random Variables, Journal of the American Statistical Association, vol.18, issue.297, pp.33-45, 1962.
DOI : 10.1214/aoms/1177730437

P. Bickel and E. Lehman, Unbiased Estimation in Convex Families, The Annals of Mathematical Statistics, vol.40, issue.5, pp.1523-1525, 1969.
DOI : 10.1214/aoms/1177697370

P. Bickel and M. Rosenblatt, On Some Global Measures of the Deviations of Density Function Estimates, The Annals of Statistics, vol.1, issue.6, pp.1071-1091, 1973.
DOI : 10.1214/aos/1176342558

P. Billingsley, Convergence of Probability Measures, 1968.
DOI : 10.1002/9780470316962

J. Bleuez and D. Bosq, Etude d'une classe d'estimateurs non paramétriques de la densité, Ann. Inst. H. Poincaré, vol.14, pp.479-498, 1978.

F. Bonvalot and N. Castelle, Strong approximation of uniform empirical process by Kiefer process, 1991.

F. Bonvalot and N. Castelle, Strong approximation of bivariate uniform empirical processes, Ann. Inst. H. Poincaré, vol.34, pp.425-480, 1999.

D. Bosq, ContributionàContributionà la théorie de l'estimation fonctionnelle, Public. Inst. Statist. Univ. Paris, 1970.

D. Bosq, Linear processes in function spaces, 2000.
DOI : 10.1007/978-1-4612-1154-9

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

J. Bretagnolle and P. Massart, Hungarian Constructions from the Nonasymptotic Viewpoint, The Annals of Probability, vol.17, issue.1, pp.239-256, 1989.
DOI : 10.1214/aop/1176991506

Y. S. Chow and H. Teicher, Probability Theory, 1978.

K. Chung, An estimate concerning the Kolmogoroff limit distribution, Transactions of the American Mathematical Society, vol.67, issue.1, pp.36-50, 1949.
DOI : 10.1090/S0002-9947-1949-0034552-5

G. Collomb, Estimation non-paramétrique de la régression par la métode du noyau, Thèse, 1976.

G. Collomb, Estimation non-paramétrique de la régression par la méthode du noyau : propriété de convergence asymptotiquement normale indépendante. Annales Scientifiques de l, pp.24-46, 1977.

G. Collomb, Quelques propriétés de la méthode du noyau pour l'estimation nonparamétrique de la régression en un point fixé, C. R. Acad. Sci. Paris A, vol.285, pp.289-292, 1977.

G. Collomb, Conditions nécessaires et suffisantes de convergence uniforme d'un estimateur de la régression, estimation des dérivées de la régression, C. R. Acad

G. Collomb, Estimation non-paramétrique de la régression : régressogramme et méthode du noyau, pp.7-781, 1978.

G. Collomb, Estimation Non-parametrique de la Regression: Revue Bibliographique, International Statistical Review / Revue Internationale de Statistique, vol.49, issue.1, pp.75-93, 1981.
DOI : 10.2307/1403039

M. Csörg?-o, P. Deheuvels, and L. Horváth, An approximation of stopped sums with applications in queueing theory, Advances in Applied Probability, vol.24, issue.03, pp.674-690, 1987.
DOI : 10.1007/BF00532688

S. Csörg?-o, Limit Behaviour of the Empirical Characteristic Function, The Annals of Probability, vol.9, issue.1, pp.130-144, 1981.
DOI : 10.1214/aop/1176994513

M. Csörg?-o and L. Horváth, Weighted approximations in probability and statistics, 1993.

M. Csörg?-o, L. Horváth, and P. Kokoszka, Approximation for bootstrapped empirical processes, Proc. Amer, pp.2457-2464, 1999.

M. Csörg?-o, L. Horváth, and J. Steinebach, Invariance Principles for Renewal Processes, The Annals of Probability, vol.15, issue.4, pp.1441-1461, 1987.
DOI : 10.1214/aop/1176991986

M. Csörg?-o and P. Révész, Strong Approximations in Probability and Statistics, 1981.

A. Acosta, Invariance Principles in Probability for Triangular Arrays of $B$-Valued Random Vectors and Some Applications, The Annals of Probability, vol.10, issue.2, pp.346-373, 1982.
DOI : 10.1214/aop/1176993862

P. Deheuvels, Strong laws for local quantile processes, The Annals of Probability, vol.25, issue.4, pp.2007-2054, 1997.
DOI : 10.1214/aop/1023481119

P. Deheuvels and M. A. Lifshits, Strassen-type functional laws for strong topologies, Probability Theory and Related Fields, vol.118, issue.2, pp.151-167, 1993.
DOI : 10.1007/BF01199317

P. Deheuvels and M. A. Lifshits, Necessary and Sufficient Conditions for the Strassen Law of the Iterated Logarithm in Nonuniform Topologies, The Annals of Probability, vol.22, issue.4, pp.1838-1856, 1994.
DOI : 10.1214/aop/1176988486

P. Deheuvels and D. M. Mason, The asymptotic behavior of sums of exponential extreme values, Bulletin des Sciences Math, vol.112, pp.211-233, 1988.

P. Deheuvels and D. M. Mason, Nonstandard Functional Laws of the Iterated Logarithm for Tail Empirical and Quantile Processes, The Annals of Probability, vol.18, issue.4, pp.1693-1722, 1990.
DOI : 10.1214/aop/1176990642

P. Deheuvels and D. M. Mason, A tail empirical process approach to some nonstandard laws of the iterated logarithm, Journal of Theoretical Probability, vol.2, issue.1, pp.53-85, 1991.
DOI : 10.1007/BF01046994

P. Deheuvels and D. M. Mason, Functional laws of the iterated logarithm for large increments of empirical and quantile processes, Stochastic Processes and their Applications, vol.43, issue.1, pp.1248-1287, 1992.
DOI : 10.1016/0304-4149(92)90080-A

P. Deheuvels and D. M. Mason, Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets, The Annals of Probability, vol.22, issue.3, pp.1619-1661, 1994.
DOI : 10.1214/aop/1176988617

P. Deheuvels and D. M. Mason, Nonstandard local empirical processes indexed by sets, Journal of Statistical Planning and Inference, vol.45, issue.1-2, pp.91-112, 1995.
DOI : 10.1016/0378-3758(94)00065-4

P. Deheuvels and J. Steinebach, Exact convergence rates in strong approximation laws for large increments of partial sums, Probability Theory and Related Fields, vol.10, issue.3, pp.369-393, 1987.
DOI : 10.1007/BF01297492

L. P. Devroye, The uniform convergence of the Nadaraya-Watson regression function estimate. Canad, J. Statist, vol.6, pp.179-191, 1979.

L. P. Devroye, On the Almost Everywhere Convergence of Nonparametric Regression Function Estimates, The Annals of Statistics, vol.9, issue.6, pp.1310-1319, 1981.
DOI : 10.1214/aos/1176345647

L. P. Devroye and T. Wagner, Distribution-Free Consistency Results in Nonparametric Discrimination and Regression Function Estimation, The Annals of Statistics, vol.8, issue.2, pp.231-239, 1979.
DOI : 10.1214/aos/1176344949

L. P. Devroye and T. Wagner, On the L 1 convergence of kernel estimators of regression functions with applications in discrimination, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.15, issue.1, pp.15-25, 1980.
DOI : 10.1007/BF00533813

J. Diebolt, Testing the functions defining a nonlinear autoregressive time series, Stochastic Proc. Appl, pp.85-106, 1990.
DOI : 10.1016/0304-4149(90)90044-S

J. Diebolt, A nonparametric test for the regression function: Asymptotic theory, Journal of Statistical Planning and Inference, vol.44, issue.1, pp.1-17, 1995.
DOI : 10.1016/0378-3758(94)00045-W

J. Diebolt and N. La¨?bla¨?b, Un principe d'invariance faible pour l'´ etude d'un test nonparamétrique relatifàrelatifà la fonction de régression, C. R. Acad. Sci. Paris, vol.312, pp.887-891, 1991.

M. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc, vol.6, 1951.

R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, Journal of Functional Analysis, vol.1, issue.3, pp.290-330, 1967.
DOI : 10.1016/0022-1236(67)90017-1

R. M. Dudley, Central Limit Theorems for Empirical Measures, The Annals of Probability, vol.6, issue.6, pp.899-929, 1978.
DOI : 10.1214/aop/1176995384

U. Einmahl and D. M. Mason, An empirical process approach to the uniform consistency of kernel-type function estimators, Journal of Theoretical Probability, vol.13, issue.1, pp.1-37, 2000.
DOI : 10.1023/A:1007769924157

R. C. Elandt-johnson and N. L. Johnson, Survival models and data analysis, 1980.
DOI : 10.1002/9781119011040

P. Erd?-os and A. Rényi, On a new law of large numbers, Journal d'Analyse Math??matique, vol.1, issue.1, pp.103-111, 1970.
DOI : 10.1007/BF02795493

W. Feller, An introduction to probability theory and its applications, 1950.

H. Finkelstein, The Law of the Iterated Logarithm for Empirical Distribution, The Annals of Mathematical Statistics, vol.42, issue.2, pp.607-615, 1971.
DOI : 10.1214/aoms/1177693410

E. Fix and J. L. Hodges, Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties, International Statistical Review / Revue Internationale de Statistique, vol.57, issue.3, 1951.
DOI : 10.2307/1403797

E. Giné and J. Zinn, Some Limit Theorems for Empirical Processes, The Annals of Probability, vol.12, issue.4, pp.929-989, 1984.
DOI : 10.1214/aop/1176993138

E. Giné and J. Zinn, Lectures on the central limit theorem for empirical processes, Probability in Banach Spaces, pp.50-113
DOI : 10.1137/1116025

W. Greblicki and A. Krzyzak, Asymptotic properties of kernel estimates of a regression function, Journal of Statistical Planning and Inference, vol.4, issue.1, pp.81-90, 1980.
DOI : 10.1016/0378-3758(80)90036-1

J. Hájek, Z. Sidák, and P. Sen, Theory of Rank Tests, 1998.

P. Hall, Laws of the iterated logarithm for nonparametric density estimators, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.3, issue.1, pp.47-61, 1981.
DOI : 10.1007/BF00531973

P. Hall, The Bootstrap and Edgeworth Expansion, 1992.
DOI : 10.1007/978-1-4612-4384-7

W. Härdle, A Law of the Iterated Logarithm for Nonparametric Regression Function Estimators, The Annals of Statistics, vol.12, issue.2, pp.624-635, 1984.
DOI : 10.1214/aos/1176346510

W. Härdle, P. Janssen, and R. Serfling, Strong Uniform Consistency Rates for Estimators of Conditional Functionals, The Annals of Statistics, vol.16, issue.4, pp.1428-1449, 1988.
DOI : 10.1214/aos/1176351047

W. Härdle and S. Luckhaus, Uniform Consistency of a Class of Regression Function Estimators, The Annals of Statistics, vol.12, issue.2, pp.612-623, 1984.
DOI : 10.1214/aos/1176346509

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1214/aoms/1177730491

J. Hoffman-jorgensen, Sums of independent Banach space valued random variables, Studia Math, vol.52, pp.159-186, 1974.

T. Höglund, A unified formulation of the central limit theorem for small and large deviations from the mean, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.10, issue.No. 1, pp.105-117, 1979.
DOI : 10.1007/BF00534343

L. Horváth, Approximations for hybrids of empirical and partial sums processes, Journal of Statistical Planning and Inference, vol.88, issue.1, pp.1-18, 2000.
DOI : 10.1016/S0378-3758(99)00207-4

L. Horváth, P. Kokoszka, and J. Steinebach, Approximations for weighted bootstrap processes with an application, Statistics & Probability Letters, vol.48, issue.1, pp.59-70, 2000.
DOI : 10.1016/S0167-7152(99)00190-X

L. Horváth and J. Steinebach, On the best approximation for bootstrapped empirical processes, Statistics & Probability Letters, vol.41, issue.2, pp.117-122, 1999.
DOI : 10.1016/S0167-7152(98)00125-4

J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, 1987.
DOI : 10.1007/978-3-662-02514-7

N. C. Jain and M. B. Marcus, Integrability of infinite sums of independent vector-valued random variables, Transactions of the American Mathematical Society, vol.212, pp.1-36, 1975.
DOI : 10.1090/S0002-9947-1975-0385995-7

J. Kuelbs and R. M. Dudley, Log Log Laws for Empirical Measures, The Annals of Probability, vol.8, issue.3, pp.405-418, 1980.
DOI : 10.1214/aop/1176994716

G. Johnston, Smooth nonparametric regression analysis, 1979.

G. Johnston, Probabilities of maximal deviations for nonparametric regression function estimates, Journal of Multivariate Analysis, vol.12, issue.3, pp.402-414, 1982.
DOI : 10.1016/0047-259X(82)90074-4

J. Kahane, Some random series of functions, 1968.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, 1997.

D. Kh, S. V. Fuk, and . Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl, vol.16, pp.643-660, 1971.

J. Kiefer, Iterated Logarithm Analogues for Sample Quantiles When P n ???0, Proc. Sixth Berkeley Symp, pp.227-244, 1972.
DOI : 10.1007/978-1-4613-8505-9_43

J. Komlós, P. Major, and G. Tusnády, An approximation of partial sums of independent RV'-s, and the sample DF. I, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.43, issue.1-2, pp.111-131, 1975.
DOI : 10.1007/BF00533093

J. Komlós, P. Major, and G. Tusnády, An approximation of partial sums of independent RV's, and the sample DF. II, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.3, issue.1, pp.33-58, 1976.
DOI : 10.1007/BF00532688

V. Konakov, Asymptotic properties of some functions of nonparametric estimates of a density function, Journal of Multivariate Analysis, vol.3, issue.4, pp.454-468, 1973.
DOI : 10.1016/0047-259X(73)90034-1

V. Konakov and V. Piterbarg, On the convergence rate of maximal deviation distribution for kernel regression estimates, Journal of Multivariate Analysis, vol.15, issue.3, pp.279-294, 1984.
DOI : 10.1016/0047-259X(84)90053-8

T. L. Lai, Reproducing kernel Hilbert spaces and the law of the iterated logarithm for Gaussian processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.16, issue.1, pp.7-19, 1974.
DOI : 10.1007/BF00533181

M. Ledoux and M. Talagrand, Some Applications of Isoperimetric Methods to Strong Limit Theorems for Sums of Independent Random Variables, The Annals of Probability, vol.18, issue.2, pp.754-789, 1990.
DOI : 10.1214/aop/1176990857

P. Lévy, Théorie de l'addition des variables aléatoires, 1937.

D. O. Loftsgaarden and C. P. Quesenberry, A Nonparametric Estimate of a Multivariate Density Function, The Annals of Mathematical Statistics, vol.36, issue.3, pp.1049-1051, 1965.
DOI : 10.1214/aoms/1177700079

E. Lukacs, Characteristics Functions, Charles Griffin and Company Ltd, 1960.

Y. Mack and B. Silverman, Weak and strong uniform consistency of kernel regression estimates, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.26, issue.No. 2, pp.405-415, 1982.
DOI : 10.1007/BF00539840

P. Major, The approximation of partial sums of independent RV's, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.2, issue.3, pp.213-220, 1976.
DOI : 10.1007/BF00532673

D. M. Mason, A strong invariance theorem for the tail empirical process, Ann. Inst. H. Poincaré Probab. Statist, vol.24, pp.491-506, 1988.

D. M. Mason, G. R. Shorack, and J. A. Wellner, Strong limit theorems for oscillation moduli of the uniform empirical process, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.10, issue.1, pp.83-97, 1983.
DOI : 10.1007/BF00534996

D. M. Mason and W. R. Van-zwet, A Refinement of the KMT Inequality for the Uniform Empirical Process, The Annals of Probability, vol.15, issue.3, pp.871-884, 1987.
DOI : 10.1214/aop/1176992070

P. Massart, Strong Approximation for Multivariate Empirical and Related Processes, Via KMT Constructions, The Annals of Probability, vol.17, issue.1, pp.266-291, 1989.
DOI : 10.1214/aop/1176991508

M. Maumy, Le comportement des oscillations du processus empirique compos??, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.12, pp.1101-1104, 2001.
DOI : 10.1016/S0764-4442(01)02185-1

M. Maumy, Sur les oscillations du processus de Poisson compos??, Comptes Rendus Mathematique, vol.334, issue.8, pp.705-708, 2002.
DOI : 10.1016/S1631-073X(02)02293-8

L. Menneteau, Functional laws of the iterated logarithm for Kiefer processes, Math. Meth. in Stat, vol.8, pp.1-21, 1999.

E. A. Nadaraya, On Estimating Regression, Theory of Probability & Its Applications, vol.9, issue.1, pp.141-142, 1964.
DOI : 10.1137/1109020

E. A. Nadaraya, On Non-Parametric Estimates of Density Functions and Regression Curves, Theory of Probability & Its Applications, vol.10, issue.1, pp.186-190, 1965.
DOI : 10.1137/1110024

E. A. Nadaraya, Remarks on Non-Parametric Estimates for Density Functions and Regression Curves, Theory of Probability & Its Applications, vol.15, issue.1, pp.134-137, 1970.
DOI : 10.1137/1115015

E. A. Nadaraya, Nonparametric estimation of probability densities and regression curves The Netherlands, 1989.

Y. Nikitin, Asymptotic Efficiency of Nonparametric Tests, 1995.
DOI : 10.1017/CBO9780511530081

K. Noda, Estimation of a regression function by the parzen kernel-type density estimators, Annals of the Institute of Statistical Mathematics, vol.3, issue.1, pp.221-234, 1976.
DOI : 10.1007/BF02504741

S. Orey and W. E. Pruitt, Sample Functions of the $N$-Parameter Wiener Process, The Annals of Probability, vol.1, issue.1, pp.138-163, 1973.
DOI : 10.1214/aop/1176997030

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

K. Pearson and A. Lee, ON THE LAWS OF INHERITANCE IN MAN: I. INHERITANCE OF PHYSICAL CHARACTERS, Biometrika, vol.2, issue.4, pp.357-462, 1903.
DOI : 10.1093/biomet/2.4.357

V. Petrov, Limit theorems of probability theory, 1995.

P. Révész, On Strong Approximation of the Multidimensional Empirical Process, The Annals of Probability, vol.4, issue.5, pp.729-743, 1976.
DOI : 10.1214/aop/1176995981

F. Riesz and B. Sz-nagy, Functional Analysis, 1955.

T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels, Stochastic Processes for Insurance and Finance, 1999.
DOI : 10.1002/9780470317044

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

M. Rosenblatt, Multivariate Analysis II, chapter Conditional probability density and regression estimators, pp.25-31, 1969.

L. Rüschendorf, Applications of empirical processes, Communications lors des Journées sur les Propriétés Asymptotiques en Statistique Non-Paramétrique, 1979.

F. H. Ruymgaart and J. A. Wellner, SOME PROPERTIES OF WEIGHTED MULTIVARIATE EMPIRICAL PROCESSES, Statistics & Risk Modeling, vol.2, issue.3-4, pp.199-223, 1984.
DOI : 10.1524/strm.1984.2.34.199

M. Schilder, Some asymptotic formulas for Wiener integrals, Transactions of the American Mathematical Society, vol.125, issue.1, pp.193-216, 1966.
DOI : 10.1090/S0002-9947-1966-0201892-6

E. F. Schuster, Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points, The Annals of Mathematical Statistics, vol.43, issue.1, pp.84-88, 1972.
DOI : 10.1214/aoms/1177692703

E. F. Schuster and S. Yakowitz, Contributions to the Theory of Nonparametric Regression, with Application to System Identification, The Annals of Statistics, vol.7, issue.1, pp.1310-1319, 1979.
DOI : 10.1214/aos/1176344560

D. W. Scott, Multivariate Density Estimation : Theory, Practice and Visualization, 1992.
DOI : 10.1002/9781118575574

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

J. Shao and D. Tu, The Jacknife and Bootstrap, 1996.

G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, 1986.
DOI : 10.1137/1.9780898719017

A. V. Skorohod, Limit Theorems for Stochastic Processes, Theory of Probability & Its Applications, vol.1, issue.3, pp.261-290, 1956.
DOI : 10.1137/1101022

N. Smirnoff, Sur lesécartslesécarts de la courbe de distribution empirique, Mat. Sbornik, vol.6, pp.3-26, 1939.

C. Spiegelman and J. Sacks, Consistent Window Estimation in Nonparametric Regression, The Annals of Statistics, vol.8, issue.2, pp.240-246, 1980.
DOI : 10.1214/aos/1176344950

C. Stone, Consistent Nonparametric Regression, The Annals of Statistics, vol.5, issue.4, pp.595-645, 1977.
DOI : 10.1214/aos/1176343886

V. Strassen, An invariance principle for the law of the iterated logarithm, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.104, issue.3, pp.221-226, 1964.
DOI : 10.1007/BF00534910

W. Stute, The Oscillation Behavior of Empirical Processes, The Annals of Probability, vol.10, issue.1, pp.86-107, 1982.
DOI : 10.1214/aop/1176993915

M. Talagrand, Donsker classes of sets. Probab. Theory Related Fields, pp.169-191, 1988.

M. S. Taqqu and C. Czado, A survey of functional laws of the iterated logarithm for self-similar processes, Communications in Statistics. Stochastic Models, vol.27, issue.1, pp.77-115, 1985.
DOI : 10.1080/15326348508807005

A. D. Ventsel, Rough Limit Theorems on Large Deviations for Markov Stochastic Processes. I, Theory of Probability & Its Applications, vol.21, issue.2, pp.227-242, 1976.
DOI : 10.1137/1121030

G. Watson, Smooth regression analysis, Sankhyã A, vol.26, pp.359-372, 1964.