DMS 9625777 Doksum This research addresses the question of how intuitive and concise linear model concepts and techniques can be extended to nonparametric settings. Nonparametric counterparts of such commonly used linear model ideas as regression coefficients, correlation coefficients, coefficient of determination, and principal components are considered. The research also studies nonparametric techniques for model diagnostics that can be used for dimensionality reduction and to address the question of adequacy of particular models. Both asymptotic and finite sample properties are studied, and the problem of developing reliable data-based methods for smoothing parameter selection for functionals and curves is addressed. %%% With the advent of computer data bases of unprecedented size and complexity and with the dramatic increase in computer power, it has become increasingly more desirable and possible to develop more flexible models, concepts, and procedures that can be used to study relationships between variables and to construct models without relying on rigid global assumptions. Much of the recent work in statistics have addressed this need for more general and flexible methods. This research further extends this work with a special focus on procedures that are counterparts of many commonly used linear model concepts and that expose important features in the data using intuitive and familiar ideas. ***
