Series of randomized complete block experiments with non-normal data

Randomized complete block designs are common in agricultural and other experiments. In this manuscript, we derive asymptotic procedures as well as finite approximations, for the analysis of data arising from series of such experiments. We do not assume normality of the data, and the within-block covariance structures can be arbitrary (no restriction to compound symmetry). The methods are specifically designed for trials with many environments and few blocks per environment, such as multi-environment trials in variety testing and plant breeding. We consider fixed and random effects models for the environment factor. The methodology takes advantage of multivariate notation, and the questions of interest are formulated as profile analysis problems. Finite performance of the proposed procedures is examined in a simulation study, and application is demonstrated using data from a series of crop variety trials.