Mathematical Sciences: A Study of Nonparametric Curve       Estimators
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Bernard McDonald', 'PO_EMAI': None, 'PO_PHON': None}
A primary objective of this research is to develop a unified               theory for nonparametric fitting of multivaritate response                      surfaces based on likelihoods for smoothing splines and kernel                  estimators.  The proposed approach involves combining the notions               of a penalized likihood and a weighted likelihood in a penalized-               weighted negative log-likelihood equation.  This will provide a                 common framework within which to study and compare the properties               of kernel estimators and smoothing splines.  Remaining objectives               address ways with which to make kernel estimators as efficient as               possible in order to prove a nonparametric alternative to the                   currently popular parametric approaches used in response surface                methodoloy.                                                                          This research is in the general area of statistical                        regression.  Much recent activity in the field has been directed                at relaxing the assumptions in regression theory and thereby                    increasing the utility of these statistical methods.  The result                of recent progress is the existance a new set of fragmented tools               for data analysis with unclear advantanges and disadvantages with               respect to each other.  This inhibits their application to other                scientific problems.  This proposal is to unify recent advances                 in this area and, thereby, provide the means to choose the most                 appropriate and informative tool for analyzing a particular data                set.
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