Handling heteroskedasticity in the linear regression model
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Date
2022
Authors
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Publisher
University of the Western Cape
Abstract
This research project delves into the problem of heteroskedasticity in the linear regression model. Having
defined the problem and its consequences for estimation and inference, a comprehensive literature
review of existing methods for diagnosing and correcting for heteroskedasticity is undertaken, with
special emphasis on heteroskedasticity tests.
New theory on the statistical properties of the Ordinary Least Squares residuals is developed, leading
to new models for estimating linear regression error variances. The most important of these models
is the Auxiliary Linear Variance Model, which is further classified into sub-types (e.g., clustering, linear,
penalised polynomial, spline). Model fitting techniques are discussed, which reduce to quadratic
programming problems. An Auxiliary Nonlinear Variance Model is also developed, which can be fitted
using a maximum quasi-likelihood method. Techniques for tuning of model hyperparameters and
feature selection are discussed. Bootstrap methods of obtaining interval estimates for error variances
are also proposed. A new heteroskedasticity test is constructed based on the auxiliary linear variance
model.
To make existing and new methods of handling heteroskedasticity more accessible to the practitioner,
a new package called skedastic has been developed for R statistical software. Its functionality
is described in detail.
Description
Philosophiae Doctor - PhD
Keywords
Bootstrap, Power, Statistics