Estimation and hypothesis testing in the two-stage nested design under nonnormality. Issue 5 (24th March 2022) - Gedik Balay, İklim and Senoglu, Birdal
Abstract : The purpose of this paper is to develop robust and efficient estimators of the parameters in the two-stage nested design under nonnormality of error distribution using modified maximum likelihood methodology proposed by Tiku (Estimating the mean and standard deviation from a censored normal sample. Biometrika. 1967;54:155–165; Estimating the parameters of normal and logistic distributions from censored samples. Aust N Z J Stat. 1968;10:64–74). New test statistics based on proposed estimators are obtained to test the factor effects. An extensive Monte-Carlo simulation study is done for comparing the proposed estimators and the tests based on them with the corresponding normal theory solutions. Simulation results show that our solutions are more efficient and robust than the normal theory solutions. At the end of the study, we analyze two different real datasets taken from the literature.