In the numerous forms of analysis of variance (ANOVA) discussed in previous chapters, variance components were estimated by equating observed mean squares to expressions describing their expected values, these being functions of the variance components. ANOVA has the nice feature that the estimators for the variance components are unbiased regardless of whether the data are normally distributed...

2. In the context of a balanced one-way random effect model where the εij’s are N = nk i.i.d. N(0, σ), εij − εi. and εi′. − ε.. are independent for all choices of i, j, and i′. Proof: It suffices to show that cov(εij − εi., εi′.− ε..) = 0 for all i, i′, and j due to normality. case 1 : i = i′. cov(εij − εi., εi. − ε..) = cov(εij, εi.) − cov(εij, ε..) − cov(εi., εi.) + cov(εi., ε..) = σ/n− σ/nk ...

Variance-component models are an indispensable tool for statisticians wanting to capture both random and fixed model effects. They have applications in a wide range of scientific disciplines. While maximum likelihood estimation (MLE) is the most popular method estimating variance-component parameters, it numerically challenging large data sets. In this article, we consider class coordinate desc...