-
作者：EFROMOVICH, S; LOW, MG
作者单位：University of Pennsylvania
摘要：Given a collection of nested closed, convex symmetric sets and a linear functional, we find estimates which are within a logarithm term of being simultaneously asymptotically minimax. Moreover, these estimates can be constructed so that the loss of this logarithm term only occurs on a small subset of functions. These estimates are quasi-optimal since there do not exist estimators which do not lose a logarithm term on some part of the parameter spaces.
-
作者：CHENG, ZM; LEBOWITZ, JL; MAJOR, P
作者单位：Rutgers University System; Rutgers University New Brunswick; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Let A be an oval with a nice boundary in R2, R a large positive number, c > 0 some fixed number and alpha a uniformly distributed random vector in the unit square [0, 1]2. We are interested in the number of lattice points in the shifted annular region consisting of the difference of the sets {(R + c/R) A - alpha} and {(R - c/R) A - alpha}. We prove that when R tends to infinity, the expectation and the variance of this random variable tend to 4c times the area of the set A, i.e. to the area of...
-
作者：USTUNEL, AS; ZAKAI, M
作者单位：Technion Israel Institute of Technology
摘要：In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space, We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series repres...
