Title page for ETD etd-1322112139711101

Type of Document Dissertation
Author Robinson, Timothy J.
URN etd-1322112139711101
Title Dual Model Robust Regression
Degree PhD
Department Statistics
Coakley, Clint W.
Myers, Raymond H.
Smith, Eric P.
Terrell, George R.
Birch, Jeffrey B. Committee Chair
Keywords
• variance estimation
• nonparametric
• regression
• dual modeling
Date of Defense 1997-04-15
Availability unrestricted
Abstract
In typical normal theory regression, the assumption of

homogeneity of variances is often not appropriate.

Instead of treating the variances as a nuisance and

transforming away the heterogeneity, the structure of

the variances may be of interest and it is desirable to

model the variances. Aitkin (1987) proposes a

parametric dual model in which a log linear

dependence of the variances on a set of explanatory

variables is assumed. Aitkin's parametric approach is

an iterative one providing estimates for the parameters

in the mean and variance models through joint

maximum likelihood. Estimation of the mean and

variance parameters are interrelatedas the responses

in the variance model are the squared residuals from

the fit to the means model. When one or both of the

models (the mean or variance model) are

misspecified, parametric dual modeling can lead to

faulty inferences. An alternative to parametric dual

modeling is to let the data completely determine the

form of the true underlying mean and variance

functions (nonparametric dual modeling). However,

nonparametric techniques often result in estimates

which are characterized by high variability and they

ignore important knowledge that the user may have

regarding the process. Mays and Birch (1996) have

demonstrated an effective semiparametric method in

the one regressor, single-model regression setting

which is a "hybrid" of parametric and nonparametric

fits. Using their techniques, we develop a dual

modeling approach which is robust to misspecification

in either or both of the two models. Examples will be

presented to illustrate the new technique, termed here

as Dual Model Robust Regression.

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