Contribution of Milton Sobel in Selection Problem Following Ethical Allocation

Abstract

In his research career of nearly six decades, Milton Sobel has made substantial contributions in several areas of statistics and mathematics. In this present discussion, I focus on the contribution of Sobel to a specific aspect of the selection problem, namely, selection following a sequential adaptive allocation. Follow-up works by Sobel himself and other researchers are also discussed in detail. The scope for further research in this area is indicated. This is only a small part of the vast contribution of Milton Sobel.

Recommended by D. S. Coad

Keywords:

• Adaptive design
• Inverse sampling
• Inverse stopping rule
• Play-the-winner rule
• Randomization
• Three hypotheses problem
• Vector-at-a-time

Subject Classification:

• 62F07
• 62F35

ACKNOWLEDGMENTS

The author wishes to acknowledge the encouragement of the editor for writing this review paper. The author also thanks two anonymous referees for their valuable suggestions and references, which enriched the paper over some earlier versions.

Notes

Recommended by D. S. Coad