  Plausibility is a formalization of exact tests for parametric models and
generalizes procedures such as Fisher's exact test. The resulting tests are
based on cumulative probabilities of the probability density function and
evaluate consistency with a parametric family while providing exact control of
the $\alpha$ level for finite sample size. Model comparisons are inefficient in
this approach. We generalize plausibility by incorporating weighing which
allows to perform model comparisons. We show that one weighing scheme is
asymptotically equivalent to the likelihood ratio test (LRT) and has finite
sample guarantees for the test size under the null hypothesis unlike the LRT.
We confirm theoretical properties in simulations that mimic the data set of our
data application. We apply the method to a retinoblastoma data set and
demonstrate a parent-of-origin effect. Weighted plausibility also has
applications in high-dimensional data analysis and P-values for penalized
regression models can be derived. We demonstrate superior performance as
compared to a data-splitting procedure in a simulation study. We apply weighted
plausibility to a high-dimensional gene expression, case-control prostate
cancer data set. We discuss the flexibility of the approach by relating
weighted plausibility to targeted learning, the bootstrap, and sparsity
selection.
