Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors
Faculty of Sciences. Mathematics and Computer Science
New York, N.Y.
Journal of mathematical analysis and applications. - New York, N.Y.
, p. 1441-1458
University of Antwerp
We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random N-vectors. We achieve this, conceptually mainly by constructing a natural approach structure on N -random vectors overlying the topology of weak convergence, and technically mainly by deducing a specific integral representation for the Hessian matrix of a solution to the Stein equation with test function View the MathML sourceet(x)=exp⁡(−i∑k=1Ntkxk), where t,x∈RNt,x∈RN.