Browsing by Author "Stephen D. Roberts, Member"

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    An Automated Procedure for Stochastic Simulation Input Modeling with Bezier Distributions
    (1998-10-14) Donovan, Marty Edwin; James R. Wilson, Chair; Stephen D. Roberts, Member; Henry L. W. Nuttle, Member
    As a means of handling the problem of input modeling forstochastic simulation experiments, we build upon previous workof Wagner and Wilson using Bézier distributions. Wagner andWilson proposed a likelihood ratio test to determine how manycontrol points (that is, parameters) a Bézier distributionshould have to adequately model sample data. In this thesis, weextend this input-modeling methodology in two directions. First,we establish the asymptotic properties of the Likelihood RatioTest (LRT) as the sample size tends to infinity. The asymptoticanalysis applies only to maximum likelihood estimation withknown endpoints and not to any other parameter estimationprocedure, nor to situations in which the endpoints of thetarget distribution are unknown. Second, we perform acomprehensive Monte Carlo evaluation of this procedure forfitting data together with other estimation procedures based onleast squares and minimum L norm estimation. In the MonteCarlo performance evaluation, several different goodness-of-fitmeasures are formulated and used to evaluate how well the fittedcumulative distribution function (CDF) compares to theempirical CDF and to the actual CDF from which the samplescame. The Monte Carlo experiments show that in addition toworking well with the method of maximum likelihood when theendpoints of the target distribution are known, the LRT alsoworks well with minimum L norm estimation and least squaresestimation; moreover, the LRT works well with suitablyconstrained versions of these three estimation methods when theendpoints are unknown and must also be estimated.
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    Improved Batching for Confidence Interval Construction in Steady-State Simulation
    (1999-03-10) Steiger, Natalie Miller; James R. Wilson, Chair; Yahya Fathi, Member; Stephen D. Roberts, Member; Len A. Stefanski, Member
    The primary objectives of this research are formulation and evaluation of an improved batch-means procedure for steady-state simulation output analysis. The new procedure yields a confidence interval for a steady-state expected response that is centered on the sample mean of a portion of the series ofsimulation-generated responses and satisfies a user-specified absolute or relative precision requirement. We concentrate on the method of nonoverlapping batch means (NOBM), which requires the sample means computed from adjacent batches of observations to be independent and identically distributed normal random variables. For increasing batch sizes and a fixed number of batches computed from a weakly dependent (phi-mixing) output process, we establish key asymptotic distributional properties of the vector of batch means and of the numerator and squared denominator of the NOBM -ratio, where the terms of the expansion are estimated via an autoregressive--moving average time series model of the batch means. An extensive experimental performance evaluation demonstrates the advantages of ASAP versus other widely used batch-means procedures.