The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes

On obtient des conditions suffisantes qui ameliorent un theoreme precedent de Pollard (1982)

[1]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[2]  R. M. Dudley,et al.  Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces , 1966 .

[3]  R. Dudley.  The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes , 1967 .

[4]  M. J. Wichura.  Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters , 1969 .

[5]  Richard M. Dudley,et al.  Sample Functions of the Gaussian Process , 1973 .

[6]  N. O'Reilly.  On the Weak Convergence of Empirical Processes in Sup-norm Metrics , 1974 .

[7]  R. Dudley.  Central Limit Theorems for Empirical Measures , 1978 .

[8]  Local sample function behavior of random fields with independent increments , 1979 .

[9]  D. Pollard.  A central limit theorem for empirical processes , 1982, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[10]  Richard M. Dudley,et al.  Invariance principles for sums of Banach space valued random elements and empirical processes , 1983 .

[11]  D. Pollard.  Convergence of stochastic processes , 1984 .

[12]  K. Alexander,et al.  Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm , 1984 .

[13]  R. Dudley.  A course on empirical processes , 1984 .

[14]  E. Giné,et al.  Some Limit Theorems for Empirical Processes , 1984 .

[15]  R. Bass.  Law of the iterated logarithm for set-indexed partial sum processes with finite variance , 1985 .

[16]  R. Pyke,et al.  The Space $D(A)$ and Weak Convergence for Set-indexed Processes , 1985 .

[17]  R. Dudley.  An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions , 1985 .

[18]  R. Pyke,et al.  A Uniform Central Limit Theorem for Set-Indexed Partial-Sum Processes with Finite Variance , 1986 .

[19]  Kenneth S. Alexander,et al.  Sample Moduli for Set-Indexed Gaussian Processes , 1986 .

[20]  K. Alexander,et al.  Rates of growth and sample moduli for weighted empirical processes indexed by sets , 1987 .

[21]  K. Alexander,et al.  Central limit theorems for stochastic processes under random entropy conditions , 1987 .

[22]  K. Alexander,et al.  The central limit theorem for weighted empirical processes indexed by sets , 1987 .