Title page for ETD etd-22820699602791


Type of Document Master's Thesis
Author Neugebauer, Shawn Patrick
URN etd-22820699602791
Title Robust Analysis of M-Estimators of Nonlinear Models
Degree Master of Science
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
Coakley, Clint W.
Reed, Jeffrey Hugh
Mili, Lamine M. Committee Chair
Keywords
  • nonlinear regression
  • nonlinear model estimation
  • robust regression
Date of Defense 1996-08-16
Availability unrestricted
Abstract

Estimation of nonlinear models finds

applications in every field of engineering and

the sciences. Much work has been done to

build solid statistical theories for its use and

interpretation. However, there has been little

analysis of the tolerance of nonlinear model

estimators to deviations from assumptions

and normality.

We focus on analyzing the robustness

properties of M-estimators of nonlinear

models by studying the effects of deviations

from assumptions and normality on these

estimators. We discuss St. Laurent and

Cook's Jacobian Leverage and identify the

relationship of the technique to the

robustness concept of influence. We derive

influence functions for M-estimators of

nonlinear models and show that influence of

position becomes, more generally, influence

of model. The result shows that, for

M-estimators, we must bound not only

influence of residual but also influence of

model. Several examples highlight the unique

problems of nonlinear model estimation and

demonstrate the utility of the influence

function.

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