An asymptotically optimal fixed-width confidence interval for the difference of two normal means |
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Authors: | Makoto Aoshima Hiroto Hyakutake Edward J Dudewicz |
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Affiliation: | 1. Department of Mathematics and Informatics , Tokyo Gakugei University , Tokyo, 184, Japan;2. Graduate School of Mathematics , Kyushu University , Fukuoka, 810, Japan;3. Department of Mathematics , Syracuse University , NY, 13244, USA |
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Abstract: | We consider the problem of providing a fixed width confidence interval for the difference of two normal means when the variances are unknown and unequal. We propose a two-stage procedure that differs from those of Chapman (1950) and Ghosll (1975). The procedure provides the desired confidence, subject to the restriction on the width, for certain values of the design parameter h. Values of h are given by the Monte Carlo rnethod for various combinations of first stage sample size and confidence level. Finally, it is shown that the procedure is asymptotically more efficient than those of Chapmail and Ghosh with respect to total sample size, as the width of the interval approaches zero. |
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Keywords: | asymptotic effciency asymptotic optimality fixed-width confidence interval Monte Carlo method two-stage procedure |
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