The Chow and Robbins Fixed Width Confidence Interval Procedure When the Second Moment Barely Does Not Exist

Abstract

We investigate the behavior of the Chow and Robbins asymptotic fixed width confidence interval procedure when the underlying i.i.d. random variables do not necessarily have a finite second moment, however, are in the domain of attraction of a normal law.

Key Words:

• Fixed width confidence intervals
• Domain of attraction of a normal law

AMS 2000 Subject Classification:

• Primary 62L10
• Secondary 62E20

Acknowledgments

The author would like to thank the referee for a careful reading of the manuscript, along with comments that helped clarify the presentation, and Evarist Giné for suggestions that led to the proof of the first part of Theorem 2. He is also grateful to Koon Woon for a number of helpful remarks. This research was completed with the support of NSA Grant MDA904-02-1-0034 and NSF Grant DMS-0203865.

Notes

Recommended by T. N. Sriram