Titlebook: High Dimensional Probability; Ernst Eberlein,Marjorie Hahn,Michel Talagrand Conference proceedings 1998 Springer Basel AG 1998 Estimator.G

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Weak Convergence of the Row Sums of a Triangular Array of Empirical Processes,r results apply to infinitesimal arrays and random series processes. We give some sufficient finite dimensional approximation conditions for the weak convergence of these processes. These conditions are necessary under quite minimal regularity assumptions.

compel

Consistency of ,-Estimators and One-Sided Bracketing,s shown that one can use one-sided brackets [., ∞). A class . of functions is called a Glivenko-Cantelli class (GCC) if the law of large numbers for empirical measures .. → . holds with respect to uniform convergence over .. A characterization of GCC’s by Talagrand (Ann. Probab., 1987) is shown to i

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Incorruptible

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On Random Measure Processes with Application to Smoothed Empirical Processes,strating both its power and its generality we apply it to derive a ULLN for smoothed empirical processes covering a former result by Yukich (1989). Finally we also present a functional central limit theorem (FCLT) for smoothed empirical processes under conditions different from those found in the li

POINT

,A Consequence For Random Polynomials of a Result of De La Peña and Montgomery-Smith,probabilities of .-statistics implies results, which are best possible up to constants, on decoupling inequalities for tail probabilities of 1) general polynomials in independent normal variables and 2) tetrahedral polynomials in any set of not necessarily symmetric independent random variables. Alt

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Distinctions Between the Regular and Empirical Central Limit Theorems for Exchangeable Random VariaIt will be shown that, unlike the i.i.d. situation, for sums of exchangeable random variables self-norming is more robust than constant norming. Necessary and sufficient conditions are provided for selfnormalizability to a normal limit and constant normalizability to limits which are either normal o

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Laws of Large Numbers and Continuity of Processes,and only if that sequence is a.s. Abel convergent to 0. That surprising equivalence between Cesaro and Abel convergence remains true in other situations, for instance when the independent r.v. ... are symmetric, but not necessarily identically distributed (see Martikainen [8], Mikosch and Norvaisa [

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