The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.
Honest exploration of intractable probability distributions via markov chain monte carlo.Statistical Science, pages 312–334
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Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains
The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.