On non-negative estimation of variance components in mixed linear models

Alternative estimators have been derived for estimating the variance components according to Iterative Almost Unbiased Estimation (IAUE). As a result two modified IAUEs are introduced. The relative performances of the proposed estimators and other estimators are studied by simulating their bias, Mean Square Error and the probability of getting negative estimates under unbalanced nested-factorial model with two fixed crossed factorial and one nested random factor. Finally the Empirical Quantile Dispersion Graph (EQDG), which provides a comprehensive picture of the quality of estimation, is depicted corresponding to all the studied methods.