On asymptotic normality of certain linear rank statistics

We consider asymptotic normality of linear rank statistics under various randomization rules met in clinical trials and designed for patients' allocation into treatment and placebo arms. Exposition relies on some general limit theorem due to McLeish (1974) which appears to be well suited for the problem considered and may be employed for other similar rules undis- cussed in the paper. Examples of applications include well known results as well as several new ones.