A study of the trade-offs between balance and randomness in various sequential sampling procedures

One of the main aspects of a sampling procedure is the design which specifies how samples are repeatedly collected. There are many circumstances where a subset of size r is repeatedly chosen from a finite population of K elements (1 $\le r < K).$ For instance, a committee or a jury of size r is repeatedly formed from a panel of size K. Another interesting case is in comparative clinical trials where eligible subjects arrive sequentially and r of the K treatments under study must be assigned immediately to the subjects. A completely random sampling scheme is free of experimental bias and provides a basis for statistical inference precision. On the other hand, a balanced sampling scheme strengthens efficiency in statistical inference procedures. We study three sequential sampling procedures, Biased Coin Design with Imbalance Tolerance, Ehrenfest Urn Design, and a Modified Ehrenfest Urn Design, in CHAPTER 2, CHAPTER 3, and CHAPTER 4, respectively. The trade-offs between balance and randomness under the three designs are analyzed.