Doctor of Philosophy
School of Mathematics and Applied Statistics
Carolan, Anthony, Partially parametric testing, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2000. https://ro.uow.edu.au/theses/2054
Parametric tests strictly speaking rely on quite rigid distributional assumptions. Nonparametric tests have wider applicability but in general are not as powerful. The tests we consider in this thesis will, in a sense, fall between the standard parametric and nonparametric tests and so might be termed partially parametric. Data are assumed to come from a broad family of distributions which includes the normal distribution. Asymptotically optimal tests using this family are derived for the one sample and multiple sample location problems and are shown, by way of simulation, to be more powerful than standard tests in a variety of situations. For symmetric data score and Wald tests are derived to compete with the one sample t test, the two sample pooled t test and with the ANOVA F test for completely randomised designs, randomised complete block designs and randomised incomplete block designs. For asymmetric data a different family of distributions is used which allows the derivation of tests for the location of modes.