| The partially linear model is appropriate for many analyses, an example of which is analysis of covariance with non-linear covariate terms. Currently, however, inference regarding the mean function for this model is limited by the fact that no methods exist for estimating error variance which do not rely upon estimation of the mean function itself.; In this dissertation we propose a difference based estimator for error variance in the partially linear model whose performance is independent of the quality of any mean function estimator. We explore its theoretical distribution properties, and in particular, show that under mild conditions it is asymptotically normally distributed. Through simulation we examine its performance relative to traditional residual based estimators as well as compare its own performance for a variety of differencing sequences.; In addition, we use this estimator as a foundation for graphical and numerical diagnostics of heteroscedasticity. We propose a test statistic for homoscedasticity and evaluate its empirical level and power through simulations in a variety of settings. Finally, we apply our estimator and test to a real data set.; We have found that the estimator proposed here performs substantially better than any that are currently available and that its performance can be optimized by careful choice of the differencing sequence. We have also found that the graphical and numerical diagnostics we propose provide a useful tool for assessing model adequacy. The ideas presented here enable inference regarding the mean function for partially linear models with greater confidence than was previously possible. |
