Asymptotics of likelihood ratio derivative estimators in simulations of highly reliable Markovian systems
Article Abstract:
The likelihood ratio method in simulations of highly reliable Markovian systems is employed to estimate derivatives of a performance measure. The study proves that certain partial derivatives in the limit can be estimated as reliably as the performance measure itself using naive simulation. This applies only if the partial derivative is linked to a component that either has one of the greatest failure rates or has a failure that can facilitate a failure transition on one of the 'most likely paths to failure.' To identify these derivatives, a sensitivity measure which can be determined for each type of component can be used. It is also shown that estimates of all derivatives can be enhanced. Lastly, the concept of 'most likely path to failure' is formalized by proving a conditional limit theorem for distributing sample paths resulting in a system failure which happens before the system reverts to the condition where all components are operational.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1995
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A note on application of SD rules to the selection of parameter estimators
Article Abstract:
Levy committed an error regarding the use of stochastic dominance (SD) rules in choosing variance estimators for normal distributions in his 1992 paper that appeared in Management Science (vol. 38, p. 555). This error was the same as the one committed by Ben Horim and Levy in an earlier work published in Communication Statistics - Theory, Methodology (vo. 11, p. 1'071). In this paper, Ben Horim and Levy introduced an erroneous second-order stochastic dominance (SSD) formula. They later proposed a corrected version of the formula in the paper 'Stochastic dominance and parameter estimation: the case of symmetric stake distributions' (Insurance: Mathematics and Economics, p. 133, 1984). Aside from repeating Ben Horim and Levy's mistake, Levy also provided an incorrect definition of SSD and third-order stochastic dominance.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1995
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Asymptotic Properties of Some Confidence Interval Estimators for Simulation Output
Article Abstract:
Theoretical properties of four interval estimators are analyzed. The estimators are based on an approach to simulation output analysis by standardizing the output time series generated by a simulation program. The comparisons are made against classical confidence interval estimators commonly used. Graphs are used to present numerical results.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1984
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