ABSTRACT
This chapter discusses the random effects models. For random effects models, the primary interest of statistical inference is on the individual variance components which are contained in the covariance matrix. The chapter focuses on the use of the analysis of variance method for obtaining estimators for variance components from balanced variance components models. It describes some of the statistical methods which are similar to those in the analysis of variance. S. C. Chow and J. Shao proposed a new estimation approach for obtaining non negative estimates for one-way random effects models. The proposed method has been shown to dominate the maximum likelihood and restricted maximum likelihood methods in the sense of smaller mean squared error. The concept of the minimum norm quadratic unbiased estimator (MINQUE) for variance components in random effects models was introduced by J. N. K. Rao. The MINQUE approach is quite different from the analysis of variance method.
