Statistica Sinica 28 (2018), 2823-2840

ON P-VALUES

Laurie Davies

University of Duisburg-Essen

Abstract: In statistics *P*-values are mostly used in the context of hypothesis testing. Software for linear regression assigns a *P*-value to every covariate which corresponds to testing the hypothesis that the "true" value of the regression coefficient is zero. In this paper several different uses and interpretations of *P*-values will be discussed ranging from the use of *P*-values as measures of approximation for parametric models, for location-scale *M*-functionals to Jeffreys' criticism of *P*-values and to the choice of covariates in linear regression without an error term. The approach is neither frequentist nor Bayesian. It is not frequentist as the *P*-values are calculated and interpreted for the data at hand, and simply being a *P*-value makes it non-Bayesian.

Key words and phrases: Approximate models, approximation regions, choice of covariates, functionals, prediction, *P*-values and approximation.