Applications of stochastic simulation in two-stage multiple comparisons with the best problem and time average variance constant estimation

In this dissertation, we study two problems. In the first part, we consider the two-stage methods for comparing alternatives using simulation. Suppose there are a finite number of alternatives to compare, with each alternative having an unknown parameter that is the basis for comparison. The parameters are to be estimated using simulation, where the alternatives are simulated independently. We develop two-stage selection and multiple-comparison procedures for simulations under a general framework. The assumptions are that each alternative has a parameter estimation process that satisfies a random- time-change central limit theorem (CLT), and there is a weakly consistent variance estimator (WCVE) for the variance constant appearing in the CLT. The framework encompasses comparing means of independent populations, functions of means, and steady-state means. One problem we consider of considerable practical interest and not handled in previous work on two-stage multiple-comparison procedures is comparing quantiles of alternative populations. We establish the asymptotic validity of our procedures as the prescribed width of the confidence intervals or indifference-zone parameter shrinks to zero. Also, for the steady-state simulation context, we compare our procedures based on WCVEs with techniques that instead use standardized time series methods. In the second part, we propose a new technique of estimating the variance parameter of a wide variety of stochastic processes. This new technique is better than the existing techniques for some standard stochastic processes in terms of bias and variance properties, since it reduces bias at the cost of no significant increase in variance.

Name thesis:degree_name

Doctor of Philosophy in Computing Sciences - (Ph.D.)

Discipline thesis:degree_discipline

Computer Science

Year

2011

Author dc:creator

• Chakrabarti, Dibyendu

Contributors dc:contributor

• Marvin K. Nakayama
• James M. Calvin
• Manish Chandra Bhattacharjee

• Statistical computing
• Stochastic simulation
• Probabilistic algorithms (including Monte Carlo)
• Probability theory
• Stochastic processes
• Numerical methods
• Computer Sciences

Repository record dc:identifier

https://digitalcommons.njit.edu/dissertations/287

OAI identifier oai:identifier

oai:digitalcommons.njit.edu:dissertations-1342