A Robust Procedure for the Fit of Oneway ANOVA Model under Adaptation on the Observed Samples

Afrifa-Yamoah, E., Okyere, Gabriel Asare, Asare-Bediako, Michael, Bashiru I.I. Saeed

Abstract: The possible dominance of basic assumption about underlying models on the analysis of data is of much concern. This study aimed develop a robust fitting procedure for one-way ANOVA models under adaption on the observed samples. Further investigation on Asymptotic Relative Efficiency (ARE) of this procedure and parametric F-test under class of continuous distributions was performed. 10,000 simulations were carried out for a one-way ANOVA model with three levels for sample sizes 5, 10, 15, and 20. Intralevel correlation coefficient ρ = 0 was considered in the these simulations. The findings revealed that the parametric F-test for oneway ANOVA model performed better than the non-parametric Adaptive test proposed for symmetric and moderate tailed distributions and then in symmetric and light tailed distributions with ARE between 2% and 55%. However, the Adaptive test outperformed the F-test in symmetric and asymmetric with varying tail weights distributions with ARE between 4% and 64%. Although, the F-test displayed superiority in efficiency in symmetric medium and light tailed distributions, the Adaptive test was more efficient in more broader class of continuous distribution.

Keywords: adaptive, selector statistic, simulation, non-parametric, continuous distribution, Asymptotic Relative Efficiency (ARE).

Pages: 534 – 553 | Full PDF Paper