A Tribute to Frank Anscombe and Random Central Limit Theorem from 1952

Abstract

We pay tribute to the remarkable work of Frank Anscombe published in 1952, who invented the random central limit theorem (random CLT). This path-breaking contribution subsequently influenced practically the whole spectrum of sequential analysis very heavily. It is a humble attempt on our part to briefly sketch the breadth of its impact by connecting Anscombe's work with some of the major developments in sequential analysis that came afterwards.

Keywords:

• Asymptotic distribution of stopping time
• Asymptotic normality
• Berry–Esseen rate
• Confidence intervals
• Distribution-free
• Maximum likelihood estimator
• Negative binomial
• Normal
• Nonparametric
• Point estimation
• Statistical ecology
• U-statistics

Subject Classifications:

• 62L10
• 62L12
• 60G50
• 62G05

ACKNOWLEDGMENTS

Thanks to the Associate Editor and other reviewers for making encouraging remarks.

Notes

Recommended by T. K. S. Solanky