Asymptotic distributions in randomization theory

The asymptotic distributions of some well-known statistics under different randomization schemes are considered in this thesis. It is shown that a simple linear statistic has an asymptotic normal distribution as sample size becomes large under randomization by any member of the symmetric group or any member of the group of the wreath product of the symmetric group of plots within blocks with the symmetric group of blocks. The result is also extended to a more appropriate statistic for the above mentioned groups. It is also shown that the previous asymptotic results in regression and experimental design can be achieved for the above mentioned groups for a more general case and under weaker conditions. The robustness of score tests in generalized linear models is also discussed. Finally; a simulation study examines how large the sample size should be to use the asymptotic results.