Sequential Interval Estimation of a Location Parameter with Fixed Width in the Nonregular Case∗

∗Dedicated to Professor Masafumi Akahira on his 60th birthday

Abstract

For a location-scale parameter family of distributions with a finite support, a sequential confidence interval with a fixed width is obtained for the location parameter, and its asymptotic consistency and efficiency are shown. Some comparisons with the Chow-Robbins procedure are also done.

Keywords:

• Coverage probability
• Extreme value
• Nonregular case
• Sequential interval estimation

Subject Classifications:

• 62L12
• 62F25

ACKNOWLEDGMENTS

The author would like to thank Professor M. Akahira of the University of Tsukuba for his valuable comments throughout the preparation of the paper. The author would also like to thank the anonymous referees for their helpful suggestions. This research was partially supported by the Ministry of Education, Science, Sports, and Culture of Japan, Grant-in-Aid for Young Scientists (B) 14740062.

Notes

¹If the support of f ₀ is (−a, b) (a ≠ b), then the normalized midrange does not converge to θ in probability as n → ∞.

²If the converging order γ is different, then the normalized midrange does not converge to θ in probability as n → ∞.

³It can be shown easily that such l ₀ exists uniquely.

Recommended by S. Chattopadhyay

∗Dedicated to Professor Masafumi Akahira on his 60th birthday