19,340 research outputs found
Asymptotic Validity of the Bayes-Inspired Indifference Zone Procedure: The Non-Normal Known Variance Case
We consider the indifference-zone (IZ) formulation of the ranking and
selection problem in which the goal is to choose an alternative with the
largest mean with guaranteed probability, as long as the difference between
this mean and the second largest exceeds a threshold. Conservatism leads
classical IZ procedures to take too many samples in problems with many
alternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed in
Frazier (2014), is less conservative than previous procedures, but its proof of
validity requires strong assumptions, specifically that samples are normal, and
variances are known with an integer multiple structure. In this paper, we show
asymptotic validity of a slight modification of the original BIZ procedure as
the difference between the best alternative and the second best goes to
zero,when the variances are known and finite, and samples are independent and
identically distributed, but not necessarily normal
Selection Procedures for Order Statistics in Empirical Economic Studies
In a presentation to the American Economics Association, McCloskey (1998) argued that "statistical significance is bankrupt" and that economists' time would be "better spent on finding out How Big Is Big". This brief survey is devoted to methods of determining "How Big Is Big". It is concerned with a rich body of literature called selection procedures, which are statistical methods that allow inference on order statistics and which enable empiricists to attach confidence levels to statements about the relative magnitudes of population parameters (i.e. How Big Is Big). Despite their prolonged existence and common use in other fields, selection procedures have gone relatively unnoticed in the field of economics, and, perhaps, their use is long overdue. The purpose of this paper is to provide a brief survey of selection procedures as an introduction to economists and econometricians and to illustrate their use in economics by discussing a few potential applications. Both simulated and empirical examples are provided.Ranking and selection, multiple comparisons, hypothesis testing
Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget
In stochastic simulation, input uncertainty (IU) is caused by the error in
estimating the input distributions using finite real-world data. When it comes
to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the
failure of many existing selection procedures. In this paper, we study R&S
under IU by allowing the possibility of acquiring additional data. Two
classical R&S formulations are extended to account for IU: (i) for fixed
confidence, we consider when data arrive sequentially so that IU can be reduced
over time; (ii) for fixed budget, a joint budget is assumed to be available for
both collecting input data and running simulations. New procedures are proposed
for each formulation using the frameworks of Sequential Elimination and Optimal
Computing Budget Allocation, with theoretical guarantees provided accordingly
(e.g., upper bound on the expected running time and finite-sample bound on the
probability of false selection). Numerical results demonstrate the
effectiveness of our procedures through a multi-stage production-inventory
problem
Modified Selection Mechanisms Designed to Help Evolution Strategies Cope with Noisy Response Surfaces
With the rise in the application of evolution strategies for simulation optimization, a better understanding of how these algorithms are affected by the stochastic output produced by simulation models is needed. At very high levels of stochastic variance in the output, evolution strategies in their standard form experience difficulty locating the optimum. The degradation of the performance of evolution strategies in the presence of very high levels of variation can be attributed to the decrease in the proportion of correctly selected solutions as parents from which offspring solutions are generated. The proportion of solutions correctly selected as parents can be increased by conducting additional replications for each solution. However, experimental evaluation suggests that a very high proportion of correctly selected solutions as parents is not required. A proportion of correctly selected solutions of around 0.75 seems sufficient for evolution strategies to perform adequately. Integrating statistical techniques into the algorithm?s selection process does help evolution strategies cope with high levels of noise. There are four categories of techniques: statistical ranking and selection techniques, multiple comparison procedures, clustering techniques, and other techniques. Experimental comparison of indifference zone selection procedure by Dudewicz and Dalal (1975), sequential procedure by Kim and Nelson (2001), Tukey?s Procedure, clustering procedure by Calsinki and Corsten (1985), and Scheffe?s procedure (1985) under similar conditions suggests that the sequential ranking and selection procedure by Kim and Nelson (2001) helps evolution strategies cope with noise using the smallest number of replications. However, all of the techniques required a rather large number of replications, which suggests that better methods are needed. Experimental results also indicate that a statistical procedure is especially required during the later generations when solutions are spaced closely together in the search space (response surface)
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