Abstract
Starting from an integral representation of reproducing kernels, we dene an inner product on bounded signed measures. The space of measures is embedded in a reproducing kernel Hilbert space and in a L 2 space. With a suitable choice of the kernel, the Euclidean associated distance on signed measures metrizes the weak convergence of probability measures. Using this framework, we obtain some rates of convergence in the CLT under independence (univariate and multivariate cases) or positive dependence (univariate case).
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