Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectorsStein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors
Faculty of Sciences. Mathematics and Computer Science
Analytical and topological structures
2016New York, N.Y., 2016
Journal of mathematical analysis and applications. - New York, N.Y.
433(2016):2, 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.