Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type



Arts and Sciences



First Advisor

Dr. Richard Charnigo


We review several nonparametric regression techniques and discuss their various strengths and weaknesses with an emphasis on derivative estimation and confidence band creation. We develop a generalized C(p) criterion for tuning parameter selection when interest lies in estimating one or more derivatives and the estimator is both linear in the observed responses and self-consistent. We propose a method for constructing simultaneous confidence bands for the mean response and one or more derivatives, where simultaneous now refers both to values of the covariate and to all derivatives under consideration. In addition we generalize the simultaneous confidence bands to account for heteroscedastic noise. Finally, we consider the characterization of nanoparticles and propose a method for identifying a proper subset of the covariate space that is most useful for characterization purposes.



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