It is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions F and based on a probability measure P holds a.s. if and only if F CLT (P ) and âˆ« F dPâ€¦ (More)

A Bernstein-type exponential inequality for (generalized) canonical U -statistics of order 2 is obtained and the Rosenthal and Hoffmann-JÃ¸rgensen inequalities for sums of independent random variablesâ€¦ (More)

We prove a concentration inequality for functions, Lipschitz with respect to the Euclidean metric, on the ball of `p , 1 â‰¤ p < 2 equipped with the normalized Lebesgue measure.

Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such thatâ€– f Î²â€–âˆž < âˆž for some 0< Î² < 1/2. Underâ€¦ (More)

It is proved that, for classes of functions F satisfying some measurability, the empirical processes indexed by F and based on P âˆˆ P(S) satisfy the central limit theorem uniformly in P âˆˆ P(S) if andâ€¦ (More)

It is proved that, for h measurable and symmetric in its arguments and Xi i.i.d., if the sequence {nâˆ’m2 âˆ‘ i1,...,imâ‰¤n ij 6=ik if j 6=k h(Xi1 ,...,Xim )}n=1, is stochastically bounded, then Eh2<âˆž andâ€¦ (More)

Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nascâ€™s for theâ€¦ (More)

LetX, Xi, iâˆˆN, be independent identically distributed random variables and let h(x,y)= h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm,â€¦ (More)

The Gaussian Correlation Conjecture states that for any two symmetric convex sets in n dimensional space and for any centered Gaussian measure on that space the measure of the intersection is greaterâ€¦ (More)