A semiparametric approach to the one-way layout

We consider m distributions in which the first m - 1 are obtained by multip licative exponential distortions of the mth distribution, which is a refere nce. The combined data from m samples, one from each distribution, are used in the semiparametric large-sample problem of estimating each distortion a nd the reference distribution and testing the hypothesis that the distribut ions are identical. The approach generalizes the classical normal-based one -way analysis of variance in the sense that it obviates the need for a comp letely specified parametric model. An advantage is that the probability den sity of the reference distribution is estimated from the combined data and not only fi om the,,mth sample. A power comparison with the t and F tests a nd with two nonparametric tests, obtained by means of a simulation, points to the merit of the present approach. The method is applied to rain-rate da ta from meteorological instruments.