The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations
Communications of the ACM
Algorithm 727: Quantile estimation using overlapping batch statistics
ACM Transactions on Mathematical Software (TOMS)
Optimal mean-squared-error batch sizes
Management Science
Simulating Stable Stochastic Systems, VI: Quantile Estimation
Journal of the ACM (JACM)
WSC' 90 Proceedings of the 22nd conference on Winter simulation
Batching methods in simulation output analysis: what we know and what we don't
WSC '96 Proceedings of the 28th conference on Winter simulation
Using quantile estimates in simulating internet queues with Pareto service times
Proceedings of the 33nd conference on Winter simulation
New simulation output analysis techniques: two-phase quantile estimation
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Simulation output analysis: a tutorial based on one research thread
WSC '04 Proceedings of the 36th conference on Winter simulation
Using parallel replications for sequential estimation of multiple steady state quantiles
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
The more plot: displaying measures of risk & error from simulation output
Proceedings of the 40th Conference on Winter Simulation
Batch variance estimators for the median of simulation output
Operations Research Letters
A new perspective on batched quantile estimation
Proceedings of the Winter Simulation Conference
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We show that although overlapping batch quantiles (OBQ) is asymptotically very similar to overlapping batch means, its performance for finite sample sizes is not. We show that the bias, the variance and the mean-squared-error of OBQ are not smooth functions of the batch size but rather cyclic. The cyclic behavior of OBQ depends on the marginal distribution, the point estimator of quantiles and the autocorrelation function and it diminishes with the sample size. We conclude that very large sample sizes and batch sizes are needed to obtain reliable standard error estimators when using OBQ, even for independently and identically distributed data.