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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/10029

Title: Comparative analysis of the effect of transformation techniques on some robust regression measures
Authors: Soku, Francis Atsu
Issue Date: 20-Jan-2017
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, 2016
URI: http://hdl.handle.net/123456789/10029
Appears in Collections:College of Science

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