p-Values: The Insight to Modern Statistical Inference

Abstract

I introduce a p-value function that derives from the continuity inherent in a wide range of regular statistical models. This provides confidence bounds and confidence sets, tests, and estimates that all reflect model continuity. The development starts with the scalar-variable scalar-parameter exponential model and extends to the vector-parameter model with scalar interest parameter, then to general regular models, and then references for testing vector interest parameters are available. The procedure does not use sufficiency but applies directly to general models, although it reproduces sufficiency-based results when sufficiency is present. The emphasis is on the coherence of the full procedure, and technical details are not emphasized.