# Statistics PhD defense: John Carl Pesko

### Event Description:

Title:

**Parametric Bootstrap and Objective Bayesian Testing with Applications to Heteroscedastic ANOVA**

Abstract:

Testing for differences in group means in the presence of heteroscedasticity (different variance terms for each group) is a problem with a rich history. Krishnamoorthy (2007) demonstrated that the parametric bootstrap (PB) approach is very effective, even for small samples. We note that there is a close relationship between the PB approach and Objective Bayesian (OB) approaches to testing, demonstrating the conditions for which the two are equivalent. PB and OB performance is compared to that of the unweighted test of Akritas & Papadatos (2004) with a simulation study. We expand our purview to testing for fixed effects in the randomized complete block design (RCBD) with subsampling when we allow for heteroscedastic error terms, proposing new solutions to this problem in the form of OB and unweighted tests, and derive the asymptotic distribution of this new unweighted test statistic. Finally, we prove a repeated sampling property and large sample property for general OB significance testing.