TY - INPR
A1 - Weizsäcker, Heinrich von
T1 - Sudakov's typical marginals, random linear functionals and a conditional central limit theorem
N2 - V.N. Sudakov [Sud78] proved that the one-dimensional marginals of a highdimensional second order measure are close to each other in most directions. Extending this and a related result in the context of projection pursuit of P. Diaconis and D. Freedman [Dia84], we give for a probability measure P and a random (a.s.) linear functional F on a Hilbert space simple sufficient conditions under which most of the one-dimensional images of P under F are close to their canonical mixture which turns out to be almost a mixed normal distribution. Using the concept of approximate conditioning we deduce a conditional central limit theorem (theorem 3) for random averages of triangular arrays of random variables which satisfy only fairly weak asymptotic orthogonality conditions.
Y1 - 1997
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/772
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-7411
ER -