الفهرس 
Linear Structural Models of Errors in Linear Regression Models
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Abstract
The fitting of a straight line to bivariate data (𝑥, 𝑦) is a common procedure,
standard linear regression theory show 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 errors in
variables model. An error in variables modelling is fundamentally different from
standard regression techniques. The problems of model fitting and parameter
estimation of straight line errors in variables model cannot be solved by generalizing a
simple linear regression model.
The thesis focuses on structural methods for correction of measurement error. In
particular, we evaluated the applicability and the behavior of these correction
techniques when different measurement error structures and sample sizes are present.
Firstly, we implemented two structural methods for correction, namely RC and
SIMEX, in the R programming language. Then, a simulation study was performed for a
simple linear regression model, considering two different distributions for the
measurement error: t-student and skew-normal. This thesis contains four chapters,
which are organized as follows:
Chapter one: contains some definitions and terms for measurement errors that were
used in the thesis.
Chapter Two: deals with previous studies that dealt with measurement errors in more
than one different estimation method to show how each method deals with
measurement errors and the assumptions to which the linear regression model is subject
to obtain the best estimation methods in dealing with measurement errors to reach the
best unbiased estimators of the linear regression model.
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Chapter Three: deals with measurement errors on the linear regression model and
some of its characteristics such as estimating bias, consistency and efficiency, as well
as presenting the capabilities in the case of the functional and structural model.
Chapter Four: deals with the use of a simulation study on the linear regression model
that contains measurement errors. The parameters of the regression model were
estimated, as well as the mean of the errors squares, and the analysis of the results
obtained using the R statistical programming language. This is in addition to the list of
references and appendices