Abstract
In practice, comparisons with the "best" are often the ones of primary interest. In this paper, parametric and nonparametric simultaneous upper confidence intervals for all distances from the "best" are derived under the location model. Their improvement upon the results of Bechhofer (1954), Gupta (1956, 1965), Fabian (1962), and Desu (1970) in the parametric case is discussed. In the nonparametric case, no comparable confidence statements were available previously.
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