Scholarly Communications Project


Robust Analysis of M-Estimators of Nonlinear Models

by

Shawn Patrick Neugebauer

Thesis submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

Approved

Lamine Mili, Chair
Jeffrey H. Reed
Clint W. Coakley

August 16, 1996
Blacksburg, Virginia


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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