M-estimators are robust estimators that give less weight to the observations that are outliers while redescending M-estimators are those estimators that are built such that extreme outliers are completely rejected. In this paper, redescending M-estimators are compared using both the Monte Carlo simulation method and the real life data to ascertain the method that is more efficient and robust when outliers are in both x and y directions. The results from the simulation study and the real life data indicate that Anekwe redescending M-estimator is more efficient and robust when outliers are in both x and y directions.
This study investigates the errors of misclassification associated with Edgeworth Series Distribution (ESD) with a view to assessing the effects of sampling from non-normality. The effects of applying a normal classificatory rule when it is actually a persistent non-normal distribution were examined. These were achieved by comparing the errors of misclassification for ESD with ND using small sample sizes at every level of skewness factor. The simulation procedure for the experiment of the study was implemented using numerical inverse interpolation method in R program to generate a uniformly distributed random variable N. A configuration size of 1000 was obtained for the two training samples drawn at every level of skewness factor (λ 3), in the range (0.00625, 0.4). This was repeated for different small sample sizes by comparing errors of misclassification of ESD with ND. The simulation results showed that the optimum probabilities of misclassification by ESD: (E 12E) decreases and (E 12E) increases, as the skewness factor (λ 3) increases. The optimum total probability of misclassification is stable as 3 λ also increases. The probability of misclassification E 12E ≥ E 12N and E 21E ≥ E 21N at every level of λ 3. Thus, the total probabilities of misclassification are not greatly affected by the skewness factor. This asserts that the normal classification procedure is robust against departure from normality.
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