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作者：HALL, P; MARRON, JS
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：This paper establishes asymptotic lower bounds which specify, in a variety of contexts, how well (in terms of relative rate of convergence) one may select the bandwidth of a kernel density estimator. These results provide important new insights concerning how the bandwidth selection problem should be considered. In particular it is shown that if the error criterion is Integrated Squared Error (ISE) then, even under very strong assumptions on the underlying density, relative error of the select...
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作者：JORGENSEN, PET; POWERS, RT
作者单位：University of Pennsylvania
摘要：Let U denote the extended Weyl algebra, U0 subset-of U, the Weyl algebra. It is well known that every element of U of the form A = SIGMA-B(k)* B(k) is positive. We prove that the converse implication also holds: Every positive element A in U has a quadratic sum factorization for some finite set of elements (B(k)) in U. The corresponding result is not true for the subalgebra U0. We identify states on U0 which do not extend to states on U. It follows from a result of Powers (and Arveson) that su...
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作者：ALBEVERIO, S; ROCKNER, M
作者单位：University of Bonn
摘要：Using the theory of Dirichlet forms on topological vector spaces we construct solutions to stochastic differential equations in infinite dimensions of the type dX(t) = dW(t) + beta(X(t)) dt for possibly very singular drifts beta. Here (X(t))t greater-than-or-equal-to 0 takes values in some topological vector space E and (W(t))t greater-than-or-equal-to 0 is an E-valued Brownian motion. We give applications in detail to (infinite volume) quantum fields where beta is e.g. a renormalized power of...
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作者：WINNICKI, J
摘要：Estimation theory for the variances of the offspring and immigration distributions in a simple branching process with immigration is developed, analogous to the estimation theory for the means given by Wei and Winnicki (1990). Conditional and weighted conditional least squares estimators are considered and their asymptotic properties for the full range of parameters are studied. Nonexistence of consistent estimators in the critical case is established, which complements analogous result of Wei...
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作者：HALL, P; HART, JD
作者单位：Texas A&M University System; Texas A&M University College Station
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作者：BERTOIN, J
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作者：FLORCHINGER, P
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作者：NUALART, D; USTUNEL, AS; ZAKAI, M
作者单位：Technion Israel Institute of Technology
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作者：LAPEYRE, B
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作者：FAGNOLA, F
