Explicit rates of convergence in the multivariate CLT for nonlinear statistics
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We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein’s method and Slepian’s smart path interpolation method. Based on certain difference operators in the theory of concentration inequalities, we obtain two explicit bounds for the rate of convergence. Applications to Rademacher functionals, the runs and quadratic forms are provided as well.
Key words and phrasesmultivariate normal approximation Stein’s method Slepian’s interpolation method difference operator
Mathematics Subject Classification60F05 62E17
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The author thanks the anonymous referee for valuable comments for improving the paper.
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