Non-informative nuisance parameter principle for weighted likelihood test using adaptive significance levels in count data - Rivera, Andrés Felipe Flórez (2020)
The usage of classical \\textit in significance tests for evaluating statistical hypotheses is a common practice among scientists of different areas of sciences. However, this practice has been widely criticized for its interpretation for many years and from many points of view due to of its misuse. Consequently, alternatives to this procedure are needed. In this work statistical hypothesis testing using weighted likelihood functions and adaptive significance levels are reviewed, with special emphasis on exploring the properties of this procedure. Specifically, it is proved that this procedure follows both the non-informative ``nuisance\'\' parameter principle and an invariance property. These properties lead to a reduced model and tractable parametric spaces that allow tackling the problem of testing hypotheses more easily. In addition, the conditional P-value is presented as a measure of evidence of the hypotheses. The proposed test is applied to test independence and diagonal symmetry on contingency tables, compare two Poisson means and to test the Hardy-Weinberg Equilibrium hypothesis. The advantages of this methodology are discussed and possible future works are suggested.