Mathematical Sciences: A Study of Nonparametric Curve Estimators

点击翻译按钮获取中文摘要

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.