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Abstract
This study is concerned with the nonnegative point estimation of variance components in the linear mixed models under the regularity conditions. Various variance components estimation methods have been discussed in details. Two new variance components estimators are proposed. The first one can be considered as a modification of the estimators proposed by Subramani (2012). However, the second estimator can be denoted as a modification of the estimator proposed by Xu and Atchley (1996). Based on a Monte Carlo simulation, the performance of the proposed estimators is studied, using nested factorial model with two crossed factors and one nested factor, relative to other variance components estimators such as Restricted Maximum Likelihood (REML) and Minimum Norm Quadratic Unbiased Estimation (MINQUE). Finally all the suggested estimators in the vignette are activated by an empirical application