Joel Zinn

Exponential and Moment Inequalities for U-Statistics

A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained, and the Rosenthal and Hoffmann-Jorgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonical.

Uniform and universal Glivenko-Cantelli classes

AbstractA class

Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities

\widetilde{F}

On the limit theorems for random variables with values in the spaces Lp (2≦p<∞)

of measurable functions on a probability space is called a Glivenko-Cantelli class if the empirical measuresPn converge to the trueP uniformly over

Central limit theorems and weak laws of large numbers in certain banach spaces

\widetilde{F}

Weighted uniform consistency of kernel density estimators

almost surely.