Pragmatic Hypotheses in the Evolution of Science

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS

Designed to have power against all alternatives, omnibus consistent tests are the primary econometric tools for testing the correct specification of parametric conditional means when there is no information about the possible alternative. The main purpose of this paper is to show that, contrary to what is generally believed, omnibus specification tests only have substantial local power against alternatives in a finite-dimensional space (usually unknown to the researcher). We call such a space theprincipal space. We characterize and estimate the principal space for Cramér–von Mises tests. These results are some of the by-products of a detailed theoretical power analysis carried out in the paper. This investigation focuses on the class of the so-called integrated consistent tests under possibly heteroskedastic time series. A Monte Carlo experiment examines the finite-sample properties of tests and estimators of preferred alternatives. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates our findings.