Exact model comparisons in the plausibility framework

We show that one weighing scheme is asymptotically equivalent to the likelihood ratio test and has finite sample guarantees for the test size under the null hypothesis unlike the LRT

Stefan Böhringer; Dietmar Lohmann

2021

Scholarcy highlights

  • Exact inference has a long tradition in the statistical literature
  • The special form of the weighting function, which is the likelihood ratio evaluated in the plausibility estimates of the free parameters, guarantees that a value of ψ is selected into the plausibility region if the observed data belongs to the probability α events close to the plausibility estimate
  • We have extended the plausibility framework by a weighing component
  • It is clear that properties from plausibility carry over to weighted plausibility as long as the weighing does not depend on the data
  • Comparing models corresponds to weighing by likelihood ratio
  • In the high-dimensional data analysis, there are some important difference between the considered plausibility tests and the lms method. lms uses models coming from a conditional lasso model. lms can thereby reject a single co-variate while controlling family-wise error rates
  • PLAUSIBLE MODEL COMPARISONS - SEPTEMBER 13, 2021 the plausibility function is stochastically larger than uniform, computing probabilities of all events proofs the lemma

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