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Does anyone help me in the following question?

I have a sequence of probability measures $\mu_n$ and know that $\mu_n$ converges narrowly to a probability measure $\mu$. Is there any way to estimate the rate of convergence as a function of $n$? In other words, I want to have an estimate for $d(\mu_n,\mu)$, for any metric $d$ that metrizes the narrow convergence, for instance the bounded lipschitz distance.

Thank you!

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    $\begingroup$ What you're looking for is a bound on the total variation distance, which is usually non-trivial. Stein's method is one way of accomplishing this in some cases. $\endgroup$
    – Alex R.
    Commented Oct 22, 2014 at 17:00

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