Comparative analysis of the effect of transformation techniques on some robust regression measures
Abstract
When the distribution of the errors in a linear model is normal, the OLSE pro-
vides reliable parameter estimates for the linear model. When errors deviate from
normality, the OLS provides unreliable estimates. This study however evaluated
the e ect of transformation techniques on some robust regression measures by
comparing four robust regression methods namely M-estimation, MM-estimation,
S-estimation and LTS estimation to the OLS estimation using the Mean Absolute
Residuals, R2, and Relative e ciencies. Data was simulated and analyzed from
a linear model under various situations where the error term has normal distri-
bution, lognormal distribution, truncated normal distribution and contaminated
normal distribution. The log and Box-Cox transformation were applied to the
simulated data before estimating and comparing parameters. The results showed
that on the average the robust methods were 2.4% more e cient than the OLSE
for the Normal case when no transformation was applied with the exception of
the SE which was 10% less e cient. For the lognormal case, the robust methods
were 26.9% more e cient under no transformation, 24.5% more e cient under log
transformation and 22.8% more e cient under Box-Cox transformation. In the
contaminated normal case, the robust methods were 6.3% more e cient under
no transformation, 5.8% more e cient under log transformation and 3.8% more
e cient under Box-Cox transformation. In the case of the truncated normal, 10%
tail truncation resulted in the robust methods being 0.6% more e cient under no
transformation and 7.2% more e cient under log and Box-Cox transformation.
Increasing the tail truncation to 20% made the robust methods 3.3% more e -
cient under no transformation and 10.8% more e cient under log and Box-Cox
transformation. Based on the study, it is recommended that, the robust methods
should be used when the basic assumptions fail. Also, the Box-Cox transfor-
mation technique should be used to linearize data if non-linear relationship is
established before using the robust methods.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fufillment of the requirement for the degree
of Master of Philosophy in Mathematical Statistics,