An alternative method for estimating the variance components in a replicated crossover study

For a uniform within sequence replicated crossover experiment, Chinchilli and Esinhart (1996) derived closed-form expressions for the maximum likelihood (ML) and restricted maximum likelihood (REML) estimators of the variance components. In this article, we exploit the characteristics of the covariance matrix for the vector variable of measurements on each subject, and derive simple expressions for the ML and REML estimators of the variance components. We show the identify of the two sets of expressions, and illustrate the new method by applying it to an example.