Necessary Analysis and Adaptive Inference

Abstract

Statistical inference is examined for the location-scale model, using nonnormal distributions for the error. The development emphasizes necessary analysis that follows as a logical consequence from the data and model alone; only the terminal parts of the analysis use the conventional criteria of estimation and testing. Inferences are obtained concerning the shape of the distribution and concerning the location and scale parameters. Illustrations are included using real and computer-generated data. The more general linear model is examined briefly. The methods extend to the case where the error distribution is unknown in the nonparametric sense; they provide a new and flexible approach to adaptive inference.