FIXED-WIDTH CONFIDENCE INTERVALS FOR CONTRASTS
IN THE MEANS

AJIT CHATURVEDI1, N. D. SHUKLA2 AND PRAMOD S. SHUKLA2

1 Department of Statistics, University of Jammu, Jammu (Tawi)-180001, India
2 Department of Statistics, Lucknow University, Lucknow-226007, India

(Received September 18, 1989; revised July 23, 1990)

Abstract.    The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147-152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of ``additional'' observations after stopping is derived, which ensures the ``exact'' probability of coverage. Moreover, two-stage, three-stage and ``modified'' sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.

Key words and phrases:    Confidence intervals, contrasts in the means, fixed-width, multi-stage estimation.

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