A Comparison of Two Approaches to Fixed-Width Confidence Interval Estimation

Abstract

The recent method of Serfling and Wackerly (1976) for constructing fixed-width confidence intervals for the center of location is extended to include M estimators. The resultant class of procedures is compared to the stopping times of Chow and Robbins (1965), as both the interval length d and intended noncoverage probability 2α converge to zero. Except in certain special cases, the stopping times are found to have different asymptotic distributions. The coverage probability of the Serfling-Wackerly class is found as d converges to zero.

Key Words:

• Sequential confidence intervals
• Stopping times
• Robust estimators