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作者：Lecue, Guillaume; Mendelson, Shahar
作者单位：Australian National University; Technion Israel Institute of Technology
摘要：Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hull of a well chosen, empirically determined subset of F is an optimal aggregation method.
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作者：Ford, Kevin
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y, infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.
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作者：Morters, Peter; Shieh, Narn-Rueih
作者单位：University of Bath; National Taiwan University
摘要：Let D subset of R-3 be the set of double points of a three-dimensional Brownian motion. We show that, if xi = xi 3(2, 2) is the intersection exponent of two packets of two independent Brownian motions, then almost surely, the phi-packing measure of D is zero if integral(0+) r(-1-xi)phi(r)(xi) dr < infinity, and infinity otherwise. As an important step in the proof we show up-to-constants estimates for the tail at zero of Brownian intersection local times in dimensions two and three.
