Robust factorial ANCOVA with LTS error distributions

Abstract

In this study, parameter estimation and hypotheses testing in the balanced factorial analysis of covariance (ANCOVA) model, when the distribution of error terms is long-tailed symmetric (LTS) are considered. The unknown model parameters are estimated using the methodology known as modified maximum likelihood (MML). New test statistics based on these estimators are also proposed for testing the main effects, interaction effect and slope parameter. Assuming LTS distributions for the error term, a Monte-Carlo simulation study is conducted to compare the efficiencies of MML estimators with corresponding least squares (LS) estimators. Power and the robustness properties of the proposed test statistics are also compared with traditional normal theory test statistics. The results of the simulation study show that MML estimators are more efficient than corresponding LS estimators. Furthermore, proposed test statistics are shown to be more powerful and robust than normal theory test statistics. In the application part, a data set, taken from the literature, is analyzed to show the implementation of the methodology presented in the study.

Keywords

• Analysis of Covariance (ANCOVA),Factorial design,Long-tailed symmetric distribution,Modified likelihood,Monte Carlo simulation,Robustness

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