In this thesis different situations are considered in which the preliminary test estimator is applied and
the performance of the preliminary test estimator under different proposed loss functions, namely
the reflected normal , linear exponential (LINEX) and bounded LINEX (BLINEX) loss functions is
evaluated. In order to motivate the use of the BLINEX loss function rather than the reflected
normal loss or the LINEX loss function, the risk for the preliminary test estimator and its component
estimators derived under BLINEX loss is compared to the risk of the preliminary test estimator and
its components estimators derived under both reflected normal loss and LINEX loss analytically (in
some sections) and computationally. It is shown that both the risk under reflected normal loss and
the risk under LINEX loss is higher than the risk under BLINEX loss. The key focus point under
consideration is the estimation of the regression coefficients of a multiple regression model under two
conditions, namely the presence of multicollinearity and linear restrictions imposed on the regression
coefficients. In order to address the multicollinearity problem, the regression coefficients were
adjusted by making use of Hoerl and Kennard’s (1970) approach in ridge regression. Furthermore,
in situations where under- or overestimation exist, symmetric loss functions will not give optimal
results and it was necessary to consider asymmetric loss functions. In the economic application,
it was shown that a loss function which is both asymmetric and bounded to ensure a maximum
upper bound for the loss, is the most appropriate function to use. In order to evaluate the effect
that different ridge parameters have on the estimation, the risk values were calculated for all three
ridge regression estimators under different conditions, namely an increase in variance, an increase
in the level of multicollinearity, an increase in the number of parameters to be estimated in the
regression model and an increase in the sample size. These results were compared to each other
and summarised for all the proposed estimators and proposed loss functions. The comparison of the
three proposed ridge regression estimators under all the proposed loss functions was also summarised
for an increase in the sample size and an increase in variance. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Statistics / PhD / Unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/43132 |
| Date | January 2014 |
| Creators | Kleyn, Judith |
| Contributors | Arashi, Mohammad, Bekker, Andriette, 1958- |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | © 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
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