Management Science
Some complexity results for zero finding for univariate functions
Journal of Complexity - Festschrift for Joseph F. Traub, Part 1
Optimal mean-squared-error batch sizes
Management Science
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Large-sample results for batch means
Management Science
Simulation output analysis via dynamic batch means
Proceedings of the 32nd conference on Winter simulation
Overlapping batch means: something for nothing?
WSC '84 Proceedings of the 16th conference on Winter simulation
Efficient Computation of Overlapping Variance Estimators for Simulation
INFORMS Journal on Computing
Statistical analysis of simulation output: state of the art
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Low bias integrated path estimators
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Simulation output analysis using integrated paths II: Low bias estimators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Performance of folded variance estimators for simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Reflected variance estimators for simulation
Proceedings of the Winter Simulation Conference
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This article considers the steady-state simulation output analysis problem for a process that satisfies a functional central limit theorem. We construct an estimator for the time-average variance constant that is based on iterated integrations of the sample path. When the observations are batched, the method generalizes the method of batch means. One advantage of the method is that it can be used without batching the observations; that is, it can allow for the process variance to be estimated at any time as the simulation runs without waiting for a fixed time horizon to complete. When used in conjunction with batching, the method can improve efficiency (the reciprocal of work times mean-squared error) compared with the standard method of batch means. In numerical experiments, efficiency improvement ranged from a factor of 1.5 (for the waiting time sequence in an M/M/1 queueing system with a single integrated path) up to a factor of 14 (for an autoregressive process and 19 integrated paths).