Date of Award
Doctor of Philosophy
Dr. Joseph W. McKean
Rank-based estimation methods provide alternatives to least squares. Estimators derived via least squares are generally not robust to aberrant observations.Rank-based methods for linear models generalize traditional Wilcoxon procedures in the simple location models and are robust.
In the usual linear model it is assumed that the errors are independent. In the case of repeated measures data several observations are taken on each experimental unit. In the case of longitudinal data the measures are taken on the same subject over time. As such an independence assumption does not seem valid. A common solution to this is to make an assumption on the form of the errors. The form we consider is that the within subject errors are exchangeable.
We first develop a transformation approach to these models. In doing so, we also obtain a robust estimate of the compound symmetry variance covariance structure. Next we develop the asymptotic theory for these rank-based estimates via a linearity result. This theory also gives us another, nontransformation, approach to these problems.
Examples discussed include one-way, two-way, and analysis of covariance problems. The focus however is on a profile analysis of the two-way repeated measures problem. We also examine the small sample properties via simulation studies.
Kloke, John, "Rank-Based Methods for Repeated Measures Data Under Exchangeable Errors" (2005). Dissertations. 1039.