Healy's sample size of two-stage procedure in heteroscedastic simultaneous inference
Aoshima (1992) has shown that Healy's two-stage procedure is more economical of the total sample size than Chatterjee's in the heteroscedastic simultaneous inference with a given accuracy on mean vectors of several normal populations. In this paper we provide the mean and the variance of Healy's total sample size. We propose to choose the initial sample size in the two-stage procedure which minimizes the expected total sample size for given length and confidence level of confidence intervals. For example, for the normal population with covariance matrix 1.2I 3, it is shown that Healy's procedure needs the minimal expected size of total sample 29 (26 for initial sample), while Chatterjee’s procedure needs 71 (53 for initial sample) to obtain a set of simultaneous confidence intervals of length 2 with 95% confidence level.