Jackknifed variance estimators for simulation output analysis

Dingec, Kemal Dincer; Alexopoulos, Christos; Goldsman, David; Wilson, James R.; Chiu, Wei-Chi; Aktaran-Kalaycı, Tûba

doi:10.1109/wsc.2015.7408187

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…The following tasks will be undertaken in the near future: (i) development and incorporation of STS area estimators with negligible small-sample bias (Dingeç et al, 2015); (ii) development of sequential procedures based on STS area estimators computed from overlapping batches of observations (Alexopoulos et al, 2007a,b); (iii) development of sequential procedures for estimating the variance parameter σ 2 ; and (iv) enhanced experimental evaluation based on queueing networks such as the Central Server Model 3 of Law and Carson (1979).…”

Section: Discussionmentioning

confidence: 99%

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

et al. 2016

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This article presents SPSTS, an automated sequential procedure for computing point and confidence-interval (CI) estimators for the steady-state mean of a simulation-generated process subject to user-specified requirements for the CI coverage probability and relative half-length. SPSTS is the first sequential method based on standardized time series (STS) area estimators of the steady-state variance parameter (i.e., the sum of covariances at all lags). Whereas its leading competitors rely on the method of batch means to remove bias due to the initial transient, estimate the variance parameter, and compute the CI, SPSTS relies on the signed areas corresponding to two orthonormal STS area variance estimators for these tasks. In successive stages of SPSTS, standard tests for normality and independence are applied to the signed areas to determine (i) the length of the warm-up period; and (ii) a batch size sufficient to ensure adequate convergence of the associated STS area variance estimators to their limiting chi-squared distributions. SPSTS's performance is compared experimentally with that of recent batch-means methods using selected test problems of varying degrees of difficulty. SPSTS performed comparatively well in terms of its average required sample size as well as the coverage and average half-length of the final CIs. ARTICLE HISTORYKEYWORDS Steady-state simulation; simulation output analysis; method of batch means; method of standardized time series; area variance estimator; nonoverlapping variance estimator; overlapping variance estimator uiie-3995r1-final.tex 1

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Section: Discussionmentioning

confidence: 99%

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

et al. 2016

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“…In Santos and Santos 5 confidence intervals are constructed from neighbor points for unreplicated data. Also Dingeç et al 37 use jackknifing in the simulation context for estimating the variance parameter of a steady-state simulation; see Miller 38 for a review on jackknifing. In this section, the jackknifing is used for obtaining confidence intervals for the unknown parameters of the metamodel, i.e., the break points and the segmented polynomial parameters.…”

Section: Choosing the Number Of Knots And Their Locationsmentioning

confidence: 99%

Construction of stochastic simulation metamodels with segmented polynomials

Santos

2021

SIMULATION

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Metamodels are an important tool in simulation analysis as they can provide insight about the behavior of the simulation response. Modeling the response with low-degree polynomial segments allows the identification of different behavior zones and the parameters still have relation with the physical world. The purpose of this paper is to extend the use of segmented polynomial functions for simulation metamodeling, where the segments have at most identical value and slope at the breaks. Our approach is to build segmented polynomials metamodels where the hypothesis of degree and continuity of splines are less exigent, allowing more flexibility of the approximation. When breaks are known, constrained least squares are used for metamodel estimation, taking into account the linear formulation of the problem. If breaks have to be estimated, the unconstrained nonlinear regression theory is used, when it can be applied. Otherwise, the estimation is performed using an iterative algorithm which is applied repeatedly in a cyclic manner for estimating the breaks, and jackknifing yields the confidence intervals.

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Lugsail lag windows for estimating time-average covariance matrices

Vats

Flegal

2021

Biometrika

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Summary Lag windows are commonly used in time series, econometrics, steady-state simulation, and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation of the underlying process, estimators of this matrix almost always exhibit significant negative bias, leading to undesirable finite-sample properties. We propose a new family of lag windows specifically designed to improve finite-sample performance by offsetting this negative bias. Any existing lag window can be adapted into a lugsail equivalent with no additional assumptions. We use these lag windows within spectral variance estimators and demonstrate their advantages in a linear regression model with autocorrelated and heteroskedastic residuals. We further employ the lugsail lag windows in weighted batch means estimators due to their computational efficiency on large simulation output. We obtain bias and variance results for these multivariate estimators and significantly weaken the mixing condition on the process. Superior finite-sample properties are illustrated in a vector autoregressive process and a Bayesian logistic regression model.

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Jackknifed variance estimators for simulation output analysis

Cited by 5 publications

References 23 publications

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

Construction of stochastic simulation metamodels with segmented polynomials

Lugsail lag windows for estimating time-average covariance matrices

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