Statistica Sinica 28 (2018), 2823-2840
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.