A Semiparametric Approach to the One-Way Layout

Abstract

We consider m distributions in which the first m − 1 are obtained by multiplicative exponential distortions of the mth distribution, which is a reference. The combined data fromm samples, one from each distribution, are used in the semiparametric large-sample problem of estimating each distortion and the reference distribution and testing the hypothesis that the distributions are identical. The approach generalizes the classical normal-based one-way analysis of variance in the sense that it obviates the need for a completely specified parametric model. An advantage is that the probability density of the reference distribution is estimated from the combined data and not only from the mth sample. A power comparison with the t and F tests and 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 data from meteorological instruments.

KEY WORDS :

• Case-control data
• Empirical likelihood
• Exponential tilt
• Logistic regression
• Reference distribution
• Smooth goodness of fit