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Abstract

This thesis concerns the estimation of the variance function in regression data when the classical assumption of constant variance is violated. We have adopted the assumption that either the variance function is parametric or is unknown but smooth. The purpose in this thesis is to develop the techniques that are currently available.

The thesis contains two major parts. After an introduction chapter, Chapters 2 and 3 discuss the parametric approach for estimating variance functions. Chapter 2 reviews in depth a large and widely scattered literature, describes the specific procedures and provides an overview of the theory employed in estimating variance functions. Chapter 3 provides detailed empirical study of these procedures.

The second part of the thesis discusses the nonparametric approach for estimating variance functions. Chapter 4 describes in detail the techniques that are involved and studies these techniques empirically revealing that the use of sample standard deviations and absolute residuals may lead to better final variance estimates. One of the techniques associated with nonparametric approach is the determination of the amount of smoothing. Chapter 5 give some analytic theory particularly for bias, providing a new criterion for determining the amount of smoothing.

Finally, Chapter 6 applies both methods to real data.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics
Departments:	Bayes Business School Bayes Business School > Actuarial Science & Insurance > Statistical Research Reports Doctoral Theses

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