| For the past three decades interest in cheaper yet competitive variance estimates in the nonparametric setting has grown to a large degree. One family of estimators which has risen to the task is the difference-based family. Unlike their residual-based counterparts, difference-based estimators do not require the estimation of a mean function and are therefore computationally cheaper. However, little research has been done which extends the effectiveness of these estimators to anything other than the simple nonparametric setting. This thesis presents the development of difference-based estimators in the repeated measurements setting for nonparametric models. Asymptotic and simulated results are explored for five new estimators: an averaging method, a single sequence method, a sample variance method, a bootstrapping method, and a hybrid method. The hybrid method is shown to be the most adaptive while the sample variance and bootstrapping methods are shown to outperform in certain cases. A practical demonstration of the methods is supplied as well as a description of fertile ground for future work. |
