On asymptotic normality of certain linear rank statistics

TL;DR

This paper investigates the asymptotic normality of linear rank statistics in clinical trial randomization schemes, utilizing a general limit theorem to establish known and new results.

Contribution

It introduces a unified approach using McLeish's limit theorem to analyze asymptotic normality across various randomization rules in clinical trials.

Findings

Established asymptotic normality for multiple randomization schemes

Unified proof technique applicable to other similar rules

Derived new results complementing existing literature

Abstract

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.