Götze, F. Lattice point problems and the central limit theorem in Euclidean spaces. (English) Zbl 0906.60023 Doc. Math., Extra Vol. ICM Berlin 1998, vol. III, 245-255 (1998); errata ibid. vol. I, 648 (1998). Summary: A number of problems in probability and statistics lead to questions about the actual error in the asymptotic approximation of nonlinear functions of the observations. Recently new methods have emerged which provide optimal bounds for statistics of quadratic type. These tools are adaptions of methods which provide sharp bounds in some high dimensional lattice point remainder problems and solve some problems concerning the distribution of values of quadratic forms. Cited in 1 ReviewCited in 5 Documents MSC: 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics 11P21 Lattice points in specified regions Keywords:Edgeworth expansion; \(U\)-statistics; ellipsoids; irrational quadratic forms PDFBibTeX XMLCite \textit{F. Götze}, Doc. Math. Extra Vol., 245--255 (1998; Zbl 0906.60023) Full Text: EuDML EMIS