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Errors in variables regression: What is the appropriate model?

Gillard, Jonathan William 2007. Errors in variables regression: What is the appropriate model? PhD Thesis, Cardiff University.

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Abstract

The fitting of a straight line to bivariate data (x,y) is a common procedure. Standard linear regression theory deals with the situation when there is only error in one variable, either x, or y. A procedure known as y on x regression fits a line where the error is assumed to be associated with the y variable, alternatively, x on y regression fits a line when the error is associated with the x variable. The model to describe the scenario when there are errors in both variables is known as an errors in variables model. Errors in variables modelling is fundamentally different from standard regression techniques. The problems of model fitting and parameter estimation of a straight line errors in variables model cannot be solved by generalising a simple linear regression model. Briefly, this thesis provides a unified framework to the fitting of a straight line errors in variables model using the method of moments. Estimators of the line using a higher moments approach have been detailed, and asymptotic variance covariance matrices of a plethora of slope estimators are provided. Simulations demonstrate that these variance covariance matrices are accurate for even small data sets. The topic of prediction is considered, with an estimator for the latent variable presented, as well as advice on the mean value of y given x via both a parametric and non-parametric approach. The problem of residuals in an errors in variables model is described, and some quick solutions given. Some examples are presented towards the end of this thesis to demonstrate how the ideas provided may be applied to real-life data sets, as well as some areas which may demand further research.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
ISBN: 9781303209703
Funders: EPSRC
Date of First Compliant Deposit: 30 March 2016
Last Modified: 04 Jun 2017 05:54
URI: http://orca.cardiff.ac.uk/id/eprint/54629

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