Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors
Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors
Faculty of Sciences. Mathematics and Computer Science

article

2016
New York, N.Y.
, 2016

Mathematics

Journal of mathematical analysis and applications. - New York, N.Y.

433(2016)
:2
, p. 1441-1458

0022-247X

E

English (eng)

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.

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