<p>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.<P>
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-19980908-212432 |
| Date | 14 October 1998 |
| Creators | Donovan, Marty Edwin |
| Contributors | James R. Wilson, Stephen D. Roberts, Henry L. W. Nuttle |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-19980908-212432 |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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