two-way ANOVA when the distribution of the error terms is skew t (vol 48, pg 287, 2019)

Celik and Senoglu (Communications in Statistics-Simulation and Computation 48 (1):287-301, 2019) proposed a two-way analysis of variance (ANOVA) model when the distribution of the error terms is skew t. They obtained the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies. They also proposed test statistics based on these estimators for testing the main hypotheses in a two-way ANOVA model. They finally compared the efficiencies of the ML and the MML estimators and the power of the test statistics with the corresponding normal theory results via a Monte Carlo simulation study. Unfortunately, they wrongly presented one of the maximum likelihood equations and consequently, some parts of the simulation results and conclusions are questionable.

Automated summary

Celik and Senoglu (2019) proposed a two-way analysis of variance (ANOVA) model with skew t-distributed error terms. They obtained estimators for the model parameters using maximum likelihood (ML) and modified maximum likelihood (MML) methodologies. Test statistics based on these estimators were also proposed for hypothesis testing in the two-way ANOVA model. Through a Monte Carlo simulation study, they compared the efficiencies of ML and MML estimators and the power of the test statistics with normal theory results. Unfortunately, there was an error in presenting one of the maximum likelihood equations in the paper, which raises questions about some of the simulation results and conclusions.