A simulation study of estimates of a first passage time distribution for a semi-Markov process.

Abstract

This thesis reports on a simulation study of parametric and nonparametric procedures for obtaining confidence intervals for the logarithm of the probability a semi-markov process enters a particular state before a fixed time t. Three estimators and confidence interval procedures are proposed and compared. The different estimators use different amounts of information about the process. The maximum likelihood estimator and its normal confidence interval procedure uses the most; the estimator based on the empirical distribution function of the observed first passage times uses the least. An estimator based on an exponential approximation to the survivor function of the first passage time uses an intermediate amount of information; confidence intervals for the last estimator are obtained using jackknife and bootstrap procedures. The maximum likelihood procedure is the most efficient if the underlying model is correct. If the model is not correct the empirical survivor function estimator appears to be best for small times and the estimator based on the exponential approximation best for large times.