Hypotheses and confidence intervals based on parametric bootstrap method

Classical tests do not provide exact solutions to even simple problems involving nuisance parameters. To overcome problem caused by nuisance parameter, parametric bootstrap (PB) approach is developed. Test variable that is distribution free of unknown parameters is obtained by using PB approach. Distribution of this test variable can provide exact inferences for problems in the presence of nuisance parameters. Generalized p-value (GPV), which looks similar to a PB is also based on Monte Carlo method. In this dissertation, it is shown that tests based on PB approaches may be used as an alternative to classical tests for hypothesis tests and confidence intervals. A new test based on parametric bootstrap and a new generalized confidence intervals based on the GPV are developed for Behrens-Fisher problem. Tests based on PB approaches and the other tests in literature are compared for one-way ANOVA with unequal variance. A new test based on PB approach is also proposed for comparing the means of two lognormal distributions. Monte Carlo simulation studies are conducted to evaluate performances of the proposed tests under different scenarios. The simulations results indicate that the tests based on PB approaches can be applied for solution of problems in the presence of nuisance parameters. Furthermore, proposed methods are applied to the real life problems taken from the literature.