Abstract
In this thesis, MANOVA problem is studied for normal random vectors whose dimension p is larger than or equal to the number of observations N. Two covariance structures are considered, the usual independence design and the split-plot design. Procedures for testing the main effects and the interaction are proposed. Their asymptotic distributions are given under both null and alternative hypotheses. Some simulation results are also provided. Finally, the procedures are applied to metagenomics datasets to study the structure of fungal species in the rhizomes of four Gastrodia species.