Browsing by Author "Soku, Francis Atsu"

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    Comparative analysis of the effect of transformation techniques on some robust regression measures
    (October 22, 2016) Soku, Francis Atsu
    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.