Asymptotic Second-Order Efficiency of a Two-Stage Procedure for Estimating a Linear Function of Normal Means

Abstract

We consider an asymptotic second-order efficiency of a two-stage procedure which was proposed to construct a fixed-width confidence interval for a linear function of normal means. It is shown that no matter how the initial sample size is chosen, the two-stage procedure does not become asymptotically second-order efficient. However, if it is possible to assume a known lower bound for each unknown variance, it is shown that a proper choice of the initial sample size enables us to make the two-stage procedure asymptotically second-order efficient.

Key Words:

• Normal populations
• Fixed-width confidence interval
• Two-stage procedure
• Asymptotic second-order efficiency

Acknowledgment

The author wishes to thank the referees for their helpful comments.

Notes

Recommended by P. Chen