Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates. James and Stein proposed an estimator of the mean vector of a p dimensional multivariate normal distribution, which produces a smaller risk than the maximum likelihood estimator if p is at least 3. In this dissertation, we also extend their idea to a nonparametric regression setting. More specifically, we present Steinized local regression estimators of p mean response functions and their derivatives. We consider different covariance structures for the error terms, and whether or not a known upper bound for the estimation bias is assumed. We also apply Steinization to compound estimation, considering the application of Steinization to both pointwise estimators (for example, as obtained through local regression) and weight functions. Finally, the new methodology introduced in this dissertation will be demonstrated on numerical data illustrating the outcomes of a laboratory experiment in which radiation induces nanoparticles to scatter evanescent waves. The patterns of scattering, as represented by derivatives of multiple mean response functions, may be used to classify nanoparticles on their sizes and structures.

The purpose of this thesis is the development of an interactive computer-generated rendering system that provides artists with the ability to create abstract paintings simply and intuitively. This system allows the user to distort a computer-generated environment using image manipulation techniques that are derived from fundamentals of expressionistic art. The primary method by which these images will be abstracted stems from the idea of several small images assembled into a collage that represents multiple viewing points rendered simultaneously. This idea has its roots in the multiple-perspective and collage techniques used by many cubist and futurist artists of the early twentieth century.

The purpose of this thesis is the development of an interactive computer-generated rendering system that provides artists with the ability to create abstract paintings simply and intuitively. This system allows the user to distort a computer-generated environment using image manipulation techniques that are derived from fundamentals of expressionistic art. The primary method by which these images will be abstracted stems from the idea of several small images assembled into a collage that represents multiple viewing points rendered simultaneously. This idea has its roots in the multiple-perspective and collage techniques used by many cubist and futurist artists of the early twentieth century.