A Central Limit Theorem For Empirical Quantiles in the Markov Chain SettingPeter W. Glynn and Shane G. Henderson Advances in Modeling and Simulation: Festschrift in honor of Pierre L’Ecuyer. Zdravko Botev, Alexander Keller, Christiane Lemieux, Bruno Tuffin, eds. Springer (2022). We provide a new proof of a central limit theorem for empirical quantiles in the positive-recurrent Markov process setting under conditions that are essentially tight. We also establish the validity of the method of nonoverlapping batch means with a fixed number of batches for interval estimation of the quantile. The conditions of these results are likely to be difficult to verify in practice, and so we also provide more easily verified sufficient conditions. |